Considering the principal values of the inverse trigonometric functions, sin^-1 ⁡( 32x+ 12 1-x^2) ,- 12

Question

Considering the principal values of the inverse trigonometric functions, sin^-1 ⁡( 32x+ 12 1-x^2) ,- 12<x< 1 2 is equal to

Accepted Answer

Correct answer: C. (c) sin^-1 ⁡( 32x+ 12 1-x^2) ,- 12<x< 1 2 Letx= cos ⁡ , ∈ ( 4 , 2 3 ) ⇒ 1-x^2= sin ⁡ as sin ⁡ >0 sin^-1( 32 cos + 12 sin )= sin^-1 ( sin( 3+ ) ) 3+ ∈ ( 7 2 , ) = sin^-1 ⁡ ( sin ⁡( -( 3+ )) ) = sin^-1 ⁡ ( sin ⁡( 2 3- ) ) = 2 3- = 2 3- cos^-1 ⁡x = 2 3-( 2- sin^-1 ⁡x)= 6+ sin^-1 ⁡x

$Considering the principal values of the inverse trigonometric functions, sin^{- 1} (\frac{3}{2} x + \frac{1}{2} 1 - x^{2}), - \frac{1}{2} < x < \frac{1}{2} is equal to$

Solution

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