Question

X,sin‐¹x +sin‐¹(1-x) =cos‐¹x

Answer 1

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Asked on October 15, 2019 by

Sophie Adhil

Solve for x:sin

−1

x+sin

−1

(1−x)=cos

−1

x.

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VIDEO EXPLANATION

ANSWER

The given equation is

sin

−1

x+sin

−1

(1−x)=cos

−1

x

⇒sin

−1

x+sin

−1

(1−x)=

2

π

−sin

−1

x

⇒sin

−1

(1−x)=

2

π

−2sin

−1

x ...... (i)

Let sin

−1

x=y

⇒x=siny

Therefore, from (i), we get

sin

−1

(1−x)=

2

π

−2y

⇒1−x=sin(

2

π

−2y)

⇒1−x=cos2y

⇒1−x=1−2sin

2

y

⇒1−x=1−2x

2

⇒2x

2

−x=0

⇒x(2x−1)=0

⇒x=0,

2

1

Since, both these values satisfy the given equation.

Hence, the solutions of the given equation are x=0,

2

1

.