Question

Sin-1x+sin-1 1\x+cos-1x+cos-1 1/x is equal to

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Answer 1

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.