Common Inverse solutions!

Geometry Level 4

1 − cos ⁡ 2 x = 2 sin ⁡ − 1 ( sin ⁡ x ) ; x ∈ [ − π , π ] \large \sqrt {1 - \cos 2x}=\sqrt{2} \sin ^{-1}(\sin x) ; \ \ x \in [-\pi, \pi] Find the number of solutions to the equation above.

4 5 1 2 ∞ \infty 3

Sankalp Jaiswal by Sankalp Jaiswal , 28, India

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1 solution

Sankalp Jaiswal
Jun 20, 2016

√(1- 1 + 2 sin ^2 x) = sin ^-1 (sin x )

|Sin x| = sin ^ -1 (sin x)

On drawing the graph of LHS and RHS ranging from -π to π, the 2 graph intersects 4 times. Hence, the answer is 4.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I believe that the answer is 3, only − π , 0 -\pi, 0 and π \pi . Can you state the 4 values?

Calvin Lin Staff - 4 years, 11 months ago

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