Inverse Trigonometric Functions Worksheets With Answers Page 11
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MATHEMATICS
α
β
⎛
⎞
−
2
2 tan
1 tan
⎜
⎟
2
⎝
2
⎠
=
–1
tan
β
α
β
α
⎛
⎞ ⎛
⎞
⎛
⎞
+
2
−
2
+
+
2
1 tan
1 tan
2 tan
1 tan
⎜
⎟ ⎜
⎟
⎜
⎟
⎝
2
⎠ ⎝
2
⎠
2
⎝
2
⎠
α
β
2
−
2 tan
1 tan
2
2
α
β
+
2
+
2
1 tan
1 tan
2
2
–1
=
tan
α
β
−
2
1 tan
2 tan
2
2
+
α
β
2
2
+
+
1 tan
1 tan
2
2
⎛
⎞
α
β
sin cos
–1
tan
⎜
⎟
=
= R.H.S.
α +
β
cos
sin
⎝
⎠
Objective type questions
Choose the correct answer from the given four options in each of the Examples 21 to 41.
Which of the following corresponds to the principal value branch of tan
?
–1
Example 21
π π
π π
⎛
⎞
⎡
⎤
−
− ⎢
,
,
⎜
⎟
(A)
(B)
⎥
⎝
2 2
⎠
⎣
2 2
⎦
π π
⎛
⎞
−
,
⎜
⎟
(D) (0, π)
(C)
– {0}
⎝
2 2
⎠
(A) is the correct answer.
Solution
The principal value branch of sec
is
–1
Example 22
π π
π
⎡
⎤
⎧ ⎫
[
]
{ }
−
−
π − ⎨ ⎬
,
0
0,
(A)
(B)
⎢
⎥
⎣
2 2
⎦
⎩ ⎭
2
π π
⎛
⎞
−
,
(C) (0, π)
⎜
⎟
(D)
⎝
2 2
⎠
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