Question

sin^-1x+sin^-1 1/x+cos^-1x+cos^-1 1/x equal to​

Answer 1

Answer:

Solve for x : sin^-1x + sin^-1 (1 - x) = cos^-1 x .

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Answer 2

Answer:

o,1/2

Step-by-step explanation:

The given equation is

sin−1x+sin−1(1−x)=cos−1x

⇒sin−1x+sin−1(1−x)=2π−sin−1x

⇒sin−1(1−x)=2π−2sin−1x      ...... (i)

Let sin−1x=y

⇒x=siny

Therefore, from (i), we get

sin−1(1−x)=2π−2y

⇒1−x=sin(2π−2y)

⇒1−x=cos2y

⇒1−x=1−2sin2y

⇒1−x=1−2x2

⇒2x2−x=0

⇒x(2x−1)=0

⇒x=0,21

Since, both these values satisfy the given equation.

Hence, the solutions of the given equation are x=0,1/2.

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