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Question
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Solution
LHS `=sin(cos^-1 3/5+sin^-1 5/13)`
`=sin[sin^-1sqrt(1-(3/5)^2)+sin^-1 5/13]`
`=sin[sin^-1 4/5+sin^-1 5/13]`
`=sin{sin^-1[4/5xxsqrt(1-(5/13)^2)+5/13xxsqrt(1-(4/5)^2)]}`
`=sin[sin^-1(48/65+15/65)]`
`=sin(sin^-1 63/65)`
`=63/65 =`RHS
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