Solve for x: \sin ^{-1}(1-x)-2 \sin ^{-1}(x)=\frac{\pi}{2}.

CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper

Section - C

Q. Nos. 27 to 32 carry 4 marks each.

Question : 27

Total: 36

Solve for x:sin‌−1(1−x)−2sin‌−1(x)=‌

Solution: 👈: Video Solution

Given that sin‌−1(1−x)−2sin‌−1x=‌

let x=sin‌y
∴sin‌−1(1−sin‌y)−2y=‌

⇒sin‌−1(1−sin‌y)=‌

+2y
⇒1−sin‌y=sin‌(‌

+2y)
⇒1−sin‌y=cos‌2‌y
⇒1−sin‌y=1−2sin‌2y‌ as ‌cos‌2‌y=1−2sin‌2y
⇒2sin‌2y−sin‌y=0
⇒2x2−x=0
⇒x(2x−1)=0
⇒x=0,2x−1=0
⇒x=0,2x=1
⇒x=0,x=‌

But x=‌

does not satisfy the given equation
∴x=0 is the solution of the given equation.

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