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Question: If \(4 \sin ^ { - 1 } x + \cos ^ { - 1 } x = \pi\)then \(x\) is equal to....

If 4sin⁡−1x+cos⁡−1x=π4 \sin ^ { - 1 } x + \cos ^ { - 1 } x = \pithen xx is equal to.

A

0

B

12\frac { 1 } { 2 }

C

−32- \frac { \sqrt { 3 } } { 2 }

D

12\frac { 1 } { \sqrt { 2 } }

Answer

12\frac { 1 } { 2 }

Explanation

Solution

We know that 4sin⁡−1x+cos⁡−1x=π4 \sin ^ { - 1 } x + \cos ^ { - 1 } x = \pi

⇒ 3sin⁡−1x+sin⁡−1x+cos⁡−1x=π3 \sin ^ { - 1 } x + \sin ^ { - 1 } x + \cos ^ { - 1 } x = \pi

⇒ 3sin⁡−1x=π−π2=π23 \sin ^ { - 1 } x = \pi - \frac { \pi } { 2 } = \frac { \pi } { 2 }

⇒ sin⁡−1x=π/6\sin ^ { - 1 } x = \pi / 6 ⇒ x=sin⁡π6=12x = \sin \frac { \pi } { 6 } = \frac { 1 } { 2 } .