Sin^-1 (1/√17)+cos^-1 (9/√85)=tan^-1 (1/2)

Question

Prove that:

Sin^-1 (1/√17) + cos^-1 (9/√85) = tan^-1 (1/2)

Answer 1

sin^-1(\(\frac1{(\sqrt{17})}\)) + cos^-1\((\frac9{\sqrt{85}})\)

 = tan^-1(\(\frac1{\sqrt{17-1}}\)) + tan^-1(\(\frac{\sqrt{85-91}}9\))

 = tan^-1(\(\frac14\)) + tan^-1(\(\frac29\))

 = tan^-1\(\left(\cfrac{\frac14+\frac29}{1-\frac14\times\frac29}\right)\)

 = tan^-1\((\frac{9+8}{36-2})\)

= tan^-1\((\frac{17}{34})\) = tan^-1(\(\frac12\))