Prove that: sin^-1 1/√5 +sin^-1 2/√5 = π/2

Question

Prove that:

\(sin^{-1}\frac{1}{\sqrt{5}}+sin^{-1}\frac{2}{\sqrt{5}}=\frac{\pi}{2}\)

Answer 1

To Prove: 

\(sin^{-1}\frac{1}{\sqrt{5}}+sin^{-1}\frac{2}{\sqrt{5}}=\frac{\pi}{2}\)

Formula Used:

\(sin^{-1}x+sin^{-1}y\)\(=sin^{-1}(x\times\sqrt{1-y^2}+y\times\sqrt{1-x^2})\)

Proof:

= RHS 

Therefore, LHS = RHS 

Hence proved.