Inverse Trigonometric FunctionHard
Question
The set of values of x, satisfying the equation tan2(sin-1 x) > 1 is -
Options
A.[- 1 , 1]
B.
C.(- 1, 1) - 
D.[ - 1, 1] - 
Solution
tan2(sin-1x) > 1
either tan(sin-1x) > 1 ⇒ sin-1x > tan-11
⇒ sin-1x > sin-1
⇒ x >
⇒ 
< x < 1
tan(sin-1x) < -1 ⇒ sin-1x < tan-1 (-1)
⇒ sin-1x < sin-1
⇒ - 1 < x < - 
so x ∈ (-1, 1) -
either tan(sin-1x) > 1 ⇒ sin-1x > tan-11
⇒ sin-1x > sin-1
⇒ x >
⇒ < x < 1tan(sin-1x) < -1 ⇒ sin-1x < tan-1 (-1)
⇒ sin-1x < sin-1
⇒ - 1 < x < - so x ∈ (-1, 1) -
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