Inverse Trigonometric Functions Worksheets With Answers Page 18
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24INVERSE TRIGONOMETRIC FUNCTIONS
35
−π
π
(B) is the correct answer. We have
≤ sin
–1
x ≤
Solution
2
2
−π
π
π
π
π
⇒
+
≤ sin
x +
≤
+
–1
2
2
2
2
2
⇒
x) ≤ π
0 ≤ sin
x + (sin
x + cos
–1
–1
–1
⇒
x ≤ π
0 ≤ 2sin
x + cos
–1
–1
The value of tan
(sec
2) + cot
(cosec
3) is
2
–1
2
–1
Example 41
(A)
5
(B)
11
(C)
13
(D)
15
(B) is the correct answer.
Solution
tan
(sec
2) + cot
(cosec
3) = sec
(sec
2) – 1 + cosec
(cosec
3) – 1
2
–1
2
–1
2
–1
2
–1
= 2
× 1 + 3
– 2 = 11.
2
2
2.3 EXERCISE
Short Answer (S.A.)
⎛
⎞
⎛
⎞
5π
13π
+
–1
–1
tan
tan
cos
cos
⎜
⎟
⎜
⎟
Find the value of
.
1.
⎝
6
⎠
⎝
6
⎠
– 3
–1
cos cos
Evaluate
.
2.
2
6
–1
cot
– 2 cot 3
7
Prove that
.
3.
4
1
1
–
–1
–1
–1
tan
–
cot
tan
sin
Find the value of
.
4.
2
3
3
⎛
2π
⎞
tan
⎜
⎟
Find the value of tan
.
–1
5.
⎝
⎠
3
–
⎛
⎞
–4
–1
tan
⎜
⎟
Show that 2tan
–1
(–3) =
+
.
6.
⎝
3
⎠
2
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