Chapter 8: Introduction of Trigonometry – Chapter-Wise Important Questions and Answers | Class 10 Mathematics CBSE Solutions
CBSE Class 10 Mathematics Chapter 8: Introduction of Trigonometry Important Questions with Solutions and Answers
Chapter 8: INTRODUCTION TO TRIGONOMETRY
SECTION = A
Multiple Choose Question and answer
Question: If 
and 
is : [2025 Standard]
(a) 
(b) 
(c) 0 (d) 1
Solution: (a)
]
Question: In a right triangle ABC , right-angle at A, If 
, then the value of
is : [2025 Standard]
(a) 4 (b) 
(c) 
(d) 
Solution: (d)
[ Given,
]
3. If 
and 
and 
, then the value of k is : [2025 Standard]
(a) 
(b) 
(c) 3 (d) – 3
Solution: (c) 3
We have, 
and 
A/Q , 
]
Question: If 
, then the value of θ is : [ 2025 Standrad]
(a) 30° (b) 45° (c) 60° (d) 90°
Solution: (c) 60°
We have, 
]
Question: If 
, then
is equal to [2025 Standard (B)]
(a) 
(b) 
(c) 
(d) 
Solution: (b)
[ We have, 
]
Question: The value of 
is : [2025 Basic]
(a) more than 1 (b) 1 (c) 0 (d) – 1
Solution: (d) – 1
[ We have, 
]
Question: The value of 
is : [2025 Basic]
(a) 1 (b) – 1 (c) 3 (d) – 2
Solution: (c) 3
[ We have, 
]
Question: If 
, then
is equal to [2025 Basic]
(a) 
(b) 4 (c) 
(d) 4 × 45°
Solution: (c)
Given, 
Now, 
]
Question: If 
, then 
is equal to : [2024 Basic]
(a) 
(b) 
(c) 
(d) 
Solution: (c) 
[ Given,
]
Question: The value of 
is : [2024 Basic]
(a) 1 (b) 
(c) 
(d) – 1
Solution: (b)
We have, 
Question: 
is equal to [2024 Basic]
(a) 
(b) 
(c) 
(d) 
Solution: (c)
[ We have, 
]
Question: If 
, then the value of 
is : [2024 Basic]
(a) 
(b) 
(c) 
(d) 
Solution: (b)
[ We have, 
and 
]
Question: If 
, then the value of (
) is : [2024 Basic]
(a) 4 (b) 
(c) 
(d) 16
Solution: (d) 16
[ Given, 
]
Question: If 
, then the value of 
is [2023 Standard]
(a) 
(b) 
(c) 3 (d) does not exist
Solution: (c) 3
[ Given, 
Now, 
]
Question: 
is equal to [2023 Standard]
(a) – 1 (b) 
(c) 
(d) 
Solution: (a) – 1
[ We have, 
]
Question: 
is equal to : [2023 Standard]
(a) – 1 (b) 1 (c) 0 (d) 2
Solution: (b) 1 .
We have, 
]
Question: 
(a) sin60° (b) cos60° (c) tan60° (d) sin30°
Solution: (b) cos60° .
[ We have , 
]
Question: If 
, then value of 
is : [2023 Basic C ]
(a) 
(b) 
(c) 
(d) 
Solution: (d)
We have, 
Now, 
]
Question: If 
, 
, then
is equal to : [2023 Basic C]
(a) 1 (b) a²b² (c) 
(d) a²+b²
Solution: (b) 
[ Given, and
We have , 
]
Question: If 
, then 
equals : [2023 Basic]
(a) 
(b) 
(c) 
(d) 
Solution: (b) ¾
[ Given,
Now, 
]
Question: 
(a) tan90° (b) 1 (c) sin45° (d) 0
Solution: (d) 0 .
[ We have , 
]
Question: 
is equal to : [2023 Basic]
(a) 9 (b) 0 (c) 8 (d) – 9
Solution: (a) 9
[ We have, 
]
Question: 
(a) – 77 (b) 1 (c) 77 (d) 0
Solution: (a) – 77
[ We have , 
]
Question: If 
, then the value of θ is : [2023 Basic]
(a) 45° (b) 60° (c) 30° (d) 90°
Solution: (b) 60°
[ We have, 
]
Question: If 
, then the value of tanθ
is :
(a) 
(b) 
(c) 
(d) 
Solution: (a)
[ We have , and 
]
Question: If
, then the value of 
is
(a) 45° (b) 30° (c) 60° (d) 90°
Solution: (d) 90° .
[ We have , 
]
Question: If 
, then the value of 
is equal to :
(a) 
(b) 
(c) 
(d) 
Solution: (c)
We have, 
]
Question: If 
, then value of 
is equal to –
(a) 0 (b) 
(c) 
(d) 
Solution: (a) 0 .
[ We have , 
]
Question: The value of 
is :
(a) 1 (b) 0 (c) 
(d) 
Solution: (b) 0
[ We have , 
]
Question: Given that 
and 
, then the value of 
is :
(a) 1 (b) 2 (c) 3 (d)
Solution: (a) 1
[ We have, 
and 
]
Question: Which of the following statement is true ?
(a) 
for all values of 
. (b) The value of 
increases as increase .
(c) The value of 
increases as increase . (d) 
is not defined for 
.
Solution: (b) The value of increases as increase .
Question: The value of 
is equal to :
(a) 
(b) 
(c) 
(d) 
Solution: (c) 
[ We have , 
]
Question: The value of 
is :
(a) 0 (b) 2 (c) – 2 (d) 1
Solution: (c) – 2
[ We have , 
]
Question: If 
, then the value of 
is equal to –
(a) 3 (b) 5 (c) 6 (d) 8
Solution: (d) 8
[ We have , 
]
Question: Which of the following statement is true ?
(a) The value of 
is always less than 1. (b) The value of 
is always greater than 1.
(c) 
for some angle θ . (d) 
for some angle θ .
Solution: (d) for some angle .
Question: If 
, then the value of 
is
(a) 1 (b) 0 (c) 3 (d) 2
Solution: (b) 0
[ We have , 
]
Question: If 
, then the value of the expression
is :
(a) 0 (b) 1 (c) (d) – 1
Solution: 1
[ We have , 
]
Question: If 
and 
, then the value of x is :
(a) 0° (b) 45° (c) 30° (d) 60°
Solution: (c) 30°
[ We have , 
]
Question: If
, then the value of
is
(a) 
(b) 
(c) 
(d) 
Solution:
[ We have , 
Question: If 
, then the value of
is equal to :
Solution: 1
[ We have , 
]
Question: If 
, then the value of
is equal to :
(a) 
(b) 
(c) 
(d) 
Solution: (c)
[ Given ,
We have, 
]
Question: If 
and 
, then the value of
is :
(a) 1 (b) 2 (c) 3 (d) 0
Solution: (d) 0
[ We have , 
]
Question: If 
, then
equals
Solution: 
[ Given , and 
]
Question: The value of 
is :
(a) 0 (b) 1 (b) 2 (d) 
Solution: (a) 0
[ We have , 
]
SECTION = B
Question: If 
; where A is an acute angle, then find the value of 
[2025 Standard]
Solution: Given, 
Question: Evaluate : 
[2025 Standard]
Solution: We have, 
Question: Prove that 
geometrically. [2025 Basic]
Solution: Let, ABC is a right-angled at B and 
Since, 
So, ABC is an isosceles triangle
Let, 
We have, 
Proved.
Question: In 
,right-angled at B , AB = 5 cm and 
. Determine the lengths of the sides BC and AC .
Solution: Given, AB = 5 cm and 
In We have, 
and 
Question: If 
, then find the values of 
and
. [2024 Basic]
Solution: Given, 
and 
Question: Prove the following trigonometric identity : 
[2025 Basic]
Solution: LHS: 
RHS.
Question: For 
and
, verify that 
[2023 Basic C]
Solution: Given, and
LHS : 
RHS: 
LHS = RHS verified .
Question: If 
, then find the value of
. [2023 Standard]
Solution: We have,
Question: If 
and
, then find the value of 
. [2023 Standard]
Solution: We have, 
Now, 
Question: If 
, then find the value of (
). [2023 Basic ]
Solution: We have, 
Now, 
Question: For 
and
, verify that : 
. [2023 Basic]
Solution: Given, and
LHS: 
RHS: 
LHS = RHS verified .
Question: Evaluate 
if 
. [2023 Standard]
Solution: Given, 
Now, 
Question: If 
, then find the value of 
. [2023 Standard]
Solution: We have, 
Now, 
Question: If 
, then show that 
[2023 Standard]
Solution: Given, 
LHS: 
RHS Proved.
Question: If A and B are acute angles such that 
and 
, then find angles A and B. [2023 Standard]
Solution: We have, 
and 
Question: If θ is an acute angle and 
, find the value of 
. [2023 Standard]
Solution: We have, 
Now, 
Question: Express the trigonometric ratios 
and 
in terms of 
.
Solution : We have , 
and 
Question: In 
, right-angled at B , 
. Determine 
Solution : In figure :
Here ,
In , we have 
and 
Question: Prove that : 
Solution: L.H.S : 
RHS. Proved.
Question: Prove that : 
Solution : LHS : 
RHS
Question: In Fig. 8.13, find 
.
Fig. 8.13
Solution : Here, 
In 
, we have 
Now , 
and 
Question: Prove that : 
Solution : L.H.S : 
R.H.S
Question: If 
and 
are acute angles such that
, then show that 
.
Solution : Given, and are acute angles of the triangle ABC .
Given , 
So, ABC is an isosceles triangle .
proved .
Question: Evaluate : 
Solution: We have,
Question: Prove that : 
Solution : LHS : 
RHS Proved.
Question: Evaluate : 
Solution: We have, 
(v) We have, 
Question: 
Solution : L.H.S. : 
R.H.S.
Question: Given 
, find
and
.
Solution : Given 
Let, 
In , we have
and 
Question: If 
and 
, find the value of 
[2010 ]
Solution: We have, 
and 
SECTION = C
Question: If 
Evaluate 
[2018]
Solution: Given, 
Now , 
Question: Prove that : 
Solution: LHS: 
RHS: 
LHS = RHS Proved.
Question: Prove that : 
[2019 ]
Solution: LHS: 
RHS Proved.
Question: Prove that 
[2020 ]
Solution: LHS : 
RHS
Question: Prove that : 
Solution: LHS: 
RHS
Question: Prove that : 
Solution: LHS: 
Question: Prove that : 
[2025 Basic]
Solution: LHS: 
RHS Proved.
Question: Let 2A+B and A+2B be acute angles such that 
and
. Find the value
. [2025 Standard]
Solution: We have,
and
[ From (i) ]
From (i) , we get 
Question: If 
and
, then prove that 
. [2025 Standard]
Solution: Given, and
LHS : 
RHS : 
LHS = RHS Proved.
Question: Prove that : 
[2000]
Solution: LHS: 
RHS Proved.
Question: Evaluate : 
[2025 Basic, 2001 C]
Solution: We have,
Question: Prove that 
[2025 Basic]
Solution: LHS: 
RHS Proved.
Question: If 
, then show that 
. [2024 Basic]
Solution: We have,
Proved.
Question: If 
, then verify that 
[2024 Basic]
Solution: Given, 
LHS: 
RHS: 
LHS = RHS verified.
Question: Prove that : 
[2024 Basic]
Solution: LHS: 
RHS Proved.
Question: Prove that : 
. [2023 Standard]
Solution: LHS: 
RHS Proved.
Question: Prove that : 
. [2023 Standard]
Solution: LHS :
RHS Proved.
Question: If 
, check whether 
or not .
Solution: Given ,
Let, 
In , we have
, 
and 
LHS: 
RHS : 
Question: Evaluate : 
[2001 C]
Solution: We have,
Question: Prove that : 
[2025 Standard]
Solution: LHS: 
RHS Proved.
Question: Prove that : 
[2005]
Solution: LHS: 
Question: Prove that : 
Solution : L.H.S. : 
R.H.S Proved.
Question: In 
, right-angled at Q , 
and
. Determine the values of 
and 
.
Solution : Here , 
In , we have
, 
and 
Question: If 
and 
,
find 
and
.
Solution : We have , 
and 
Putting 
in equation
, we have
Therefore , the value of A and B are 45° and 15° respectively .
Question: If 
, 
and 
, 
then find 
and 
.
Solution: We have,
and
Putting 
in (i) , we get 
Therefore, the value of and 
.
Question: If 
, then evaluate 
[2009]
Solution: Given,
Now, 
Question: Prove the following : 
[2010]
Solution: LHS: 
RHS Proved.
Question: Prove that : 
Solution : L.H.S. : 
R.H.S. Proved.
Question: Prove that : 
Solution : LHS : 
RHS : 
LHS = RHS
Question: Prove that : 
Solution : L.H.S : 
R.H.S
SECTION = D
Question: Given that 
, Prove that 
[2025 Standard]
Solution: Given, 
Proved.
Question: Prove that : 
.
Solution: LHS : 
RHS
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