Inverse Trigonometric Functions Worksheets With Answers Page 13
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MATHEMATICS
1
−
2
1 x
(C)
(D)
.
x
x
x = θ, then sinθ = x
(D) is the correct answer. Let sin
–1
Solution
1
1
⇒
cosec θ =
⇒
θ =
cosec
2
2
x
x
1
−
2
1 x
⇒
θ =
⇒ cotθ =
1 + cot
2
.
2
x
x
π
for some x ∈ R, then the value of cot
If tan
x is
–1
–1
Example 27
x =
10
π
π
π
π
2
3
4
(A)
(B)
(C)
(D)
5
5
5
5
π
(B) is the correct answer. We know tan
–1
x + cot
–1
x =
. Therefore
Solution
2
π
π
cot
x =
–1
–
2
10
π
π
π
2
⇒ cot
–1
x =
–
=
.
2
10
5
The domain of sin
2x is
–1
Example 28
(A) [0, 1]
(B) [– 1, 1]
⎡
1 1
⎤
− ⎢
,
(C)
(D) [–2, 2]
⎥
⎣
2 2
⎦
2x = θ so that 2x = sin θ.
(C) is the correct answer. Let sin
–1
Solution
1
1
− ≤
≤
Now – 1 ≤ sin θ ≤ 1, i.e.,– 1 ≤ 2x ≤ 1 which gives
.
x
2
2
⎛
⎞
−
3
⎜
⎟
The principal value of sin
is
–1
⎜
⎟
Example 29
2
⎝
⎠
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