Inverse Trigonometric Functions Worksheets With Answers Page 14
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24INVERSE TRIGONOMETRIC FUNCTIONS
31
π
π
π
π
2
4
5
−
−
(A)
(B)
(C)
(D)
.
3
3
3
3
(B) is the correct answer.
Solution
⎛
⎞
−
π
π
π
3
⎛
⎞
⎛
⎞
–1
=
–1
=
–1
=
sin
⎜
⎟
sin
– sin
– sin
sin
–
⎜
⎟
⎜
⎟
.
⎜
⎟
2
⎝
3
⎠
⎝
3
⎠
3
⎝
⎠
The greatest and least values of (sin
+
(cos
are respectively
–1
2
–1
2
Example 30
x)
x)
π
−π
2
2
π
π
5
and
and
(A)
(B)
2
2
4
8
π
2
−π
2
π
2
and
and 0
(C)
(D)
.
4
4
4
(A) is the correct answer.
We have
Solution
(sin
+
(cos
=
(sin
cos
– 2 sin
x cos
–1
2
–1
2
–1
–1
2
–1
–1
x)
x)
x +
x)
x
π
2
π
⎛
⎞
−
–1
−
–1
2sin
sin
⎜
⎟
x
x
=
4
⎝
2
⎠
π
2
(
)
2
− π
–1
+
–1
sin
2 sin
x
x
=
4
⎡
⎤
2
π
π
(
)
2
–1
–1
−
+
2 sin
sin
⎢
⎥
x
x
=
2
8
⎣
⎦
⎡
⎤
2
2
π
π
⎛
⎞
–1
−
+
⎢
⎥
2 sin
⎜
⎟
x
=
.
⎝
4
⎠
16
⎢
⎥
⎣
⎦
⎡
⎤
2
2
⎛
⎞
−π π
π
2
2
⎛
⎞
π
π
−
+
2
⎢
⎥
2
i.e.
⎜
⎟
⎜
⎟
Thus, the least value is
and the Greatest value is
,
⎝
2
4
⎠
16
16
8
⎢
⎥
⎝
⎠
⎣
⎦
2
π
5
i.e.
.
4
Let θ = sin
(sin (– 600°), then value of θ is
–1
Example 31
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