Prove that: cos^-1 4/5 + sin^-1 3/5 = sin^-1 27/11

Question

Prove that:

\(cos^{-1}\frac{4}{5}+sin^{-1}\frac{3}{5}=sin^{-1}\frac{27}{11}\)

Answer 1

 Prove that:

\(cos^{-1}\frac{4}{5}+sin^{-1}\frac{3}{5}=sin^{-1}\frac{27}{11}\)

Formula Used:

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

Proof:

Substituting in (1), we get