Question

sin-1 x + sin-1 (1-x) = cos-1 x​

Answer 1

Answer:

sin^1(x)+sin^1(1-x)=cos^1(x)

sin^(1-x)=cos^1x-sin^1x

(1-x)=sin[cos^1x-sin^1x]

Using,

sin^1x+cos^x=π/2

so,(1-x)=sin[π/2-2sin^1x

=cos(2sin^1x)=cosx

cos^1(1-2x°)

using,2sinx=cos^1(1-2x squre)

so

(1-x)=(1-2x squre)

2x squre- x=0

so 2x squre- x=o

x=0,x=1/2

now put into original solution,we get

x=1/2& x=0 satisfy the given equation