Prove that: cos^-1 4/5 + cos ^-1 12/13 = cos^-1 33/65

Question

Prove that:

\(cos^{-1}\frac{4}{5}+cos^{-1}\frac{12}{13}=cos^{-1}\frac{33}{65}\)

Answer 1

To Prove:

\(cos^{-1}\frac{4}{5}+cos^{-1}\frac{12}{13}=cos^{-1}\frac{33}{65}\)

Formula Used:

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

Proof:

= RHS 

Therefore, LHS = RHS 

Hence proved.