Inverse Trigonometric Functions Worksheets With Answers Page 17
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MATHEMATICS
⎛
⎞
4 1
+
⎜
⎟
⎛
⎞
19
19
3 4
.
–1
=
=
tan tan
⎜
⎟
⎜
⎟
= tan tan
–1
4 1
⎝
8
⎠
8
⎜
⎟
− ×
1
⎝
⎠
3 4
The value of the expression sin [cot
(cos (tan
1))] is
–1
–1
Example 38
1
2
(A)
0
(B)
1
(C)
(D)
.
3
3
(D) is the correct answer.
Solution
⎡
⎤
2
2
π
1
–1
=
sin sin
⎢
⎥
sin [cot
–1
(cos
)] = sin [cot
–1
]=
3
3
4
2
⎣
⎦
⎛
⎞
1
⎜
⎟
The equation tan
x – cot
x = tan
has
–1
–1
–1
Example 39
⎝
⎠
3
(A)
no solution
(B)
unique solution
(C)
infinite number of solutions
(D)
two solutions
(B) is the correct answer. We have
Solution
π
π
tan
–1
x – cot
–1
x =
and tan
–1
x + cot
–1
x =
6
2
π
2
Adding them, we get 2tan
x =
–1
3
π
⇒ tan
x =
i.e.,
x =
.
–1
3
3
α ≤ sin
x ≤β , then
If
2
x + cos
–1
–1
Example 40
−π
π
α =
β=
,
α =
β = π
(A)
(B)
0,
2
2
−π
π
3
α =
β =
,
α =
β = π
(C)
(D)
0,
2
2
2
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