Question

4 sin^-1x+cos^-1x=pi then what is the value of x

Answer 1

As we know sin^-1x + cos^-1x is π÷2(The proof is a bit lengthy
4 sin^-1x can be written as 3 sin inverse x + sin inverse x
Therefore 4 sin inverse x + cos inverse x can be written as 3 sin inverse x + sin inverse x +cos inverse x=π
which will be 3 sin inverse x +π÷2=π
=>3 sin inverse x = π÷2
=>sin inverse x =π÷6
$x = \sin( \frac{\pi}{6} )$
x=1÷2 or x=0.5