Class 12 ISC Inverse Trigonometric Functions Important Questions
Inverse Trigonometric Functions for Class 12 includes the major concepts related to the inverse of trigonometric functions, which will help the students score good marks in their examinations. The inverse trigonometric functions play an essential role in calculus, for they serve to define many integrals. The concepts of inverse trigonometric functions are also used in science and engineering.
class 12 ISC Inverse Trignometric Functions ImportantQuestions
Inverse Trigonometric Functions ImportantQues
Q1
cot-1
(- 
1
/
√3
)
Solution
Q2
sec-1
(- 
2
/
√3
)
Solution
Q3
sin-1(-1)
Solution
Q4
cos-1
(cos 
4π
/
3
)
Solution
Q5
sin-1
(sin 
2π
/
3
)
Solution
Q6
tan-1
(tan 
3π
/
4
)
Solution
Q7
tan-1
(tan 
5π
/
6
) ≠
5π
/
6
, What is its value
Solution
Q8
sin-1
(sin 
5π
/
3
) ≠
5π
/
3
, What is its value
Solution
Q9
Find the domain of sin-1 ( 1 - x)
Solution
Q10
Find the domain of sec-1 (2x - 3)
Solution
Q11
sin
(2 sin -1
3
/
5
)
Solution
Q12
sin
(2 cos -1(- 
3
/
5
))
Solution
Q13
sin
(2 cot -1(- 
5
/
12
))
Solution
Q14
tan-1
(tan 
5π
/
6
) + cos-1
(cos
13π
/
6
)
Solution
Q15
tan-1
(- 
1
/
√3
) + cot-1
(-
1
/
√3
) + tan-1
(sin ( -
π
/
2
))
Solution
Q16
Write the following in the simplest form :
cot-1 (√1 + x2 - x) Solution
cot-1 (√1 + x2 - x) Solution
Q17
Write the following in the simplest form :
tan-1 (
tan-1 (
3 a2x - x3
/
a3 - 3ax2
)
Solution
Q18
Find the value of :
tan-1 (
tan-1 (
x
/
y
) - tan-1
(
x-y
/
x + y
)
Solution
Q19
cos-1
( 
3
/
5
cosx +
4
/
5
sinx)
Solution
Q20
Prove that :
cos (tan-1 ( sin (cot-1))) = √
cos (tan-1 ( sin (cot-1))) = √
1 + x2
/
2 + x2
Solution
Q21
Prove that cot-1 7 + cot-1 8 + cot-1 18 = cot-1 3
Solution
Q22
Prove that tan-1 1 + tan-1 2 + tan-1 3 = π
Solution
Q23
Prove that : 4(cot-1 3 + cosec-1 √) = π
Solution
Q24
Prove the following :
tan-1
tan-1
1
/
4
+ tan-1
2
/
9
= cos-1
2
/
√5
Solution
Q25
Prove the following :
tan-1
tan-1
1
/
4
+ tan-1
2
/
9
=
1
/
2
sin-1
4
/
5
Solution
Q26
If sin-1x + sin-1 y + sin-1 z = π then prove that :
(i) x2 - y2 - z2 + 2yz √ 1 - x2 = 0
(ii) x4 + y4 + z4 + 4x2 y2 z2 = 2 (x2 y2 + y2 z2 + z2 x2) Solution
(i) x2 - y2 - z2 + 2yz √ 1 - x2 = 0
(ii) x4 + y4 + z4 + 4x2 y2 z2 = 2 (x2 y2 + y2 z2 + z2 x2) Solution
Q27
Evaluate :
sin-1
( sin(10))
Solution
Q28
Evaluate :
tan-1
(tan(-6))
Solution
Q29
cos-1
(cos(- 
5π
/
6
)) ≠
- π
/
6
, What is its value
Solution
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