How do you prove $cos^-1(x)=pi/2-sin^-1(x)$ ?

Question

11767 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-27T05:24:38

Let, $sin^(-1)x=theta$ ; then $sintheta=x$

now, $sinθ = cos( π/2 - θ)=x$ and $cos^(-1)x= π/2 - θ$

therefore, $sin^(-1)x+cos^(-1)x= θ+π/2 - θ= π/2$

How do you prove cos^-1(x)=pi/2-sin^-1(x)cos^-1(x)=pi/2-sin^-1(x)?