Prove that:`sin^(-1)(8/17)+sin^(-1)(3/5)=tan^(-1)(77/36)`

1.	Prove that:`sin^(-1)(8/17)+sin^(-1)(3/5)=tan^(-1)(77/36)`
Answer» Let, `sin^-1(8/17) = x` and `sin^-1(3/5) = y->(1)` Then, `sin x = 8/17 and sin y = 3/5` If we create right angle triangles for x and y, we get `tan x = 8/15 and tan y = 3/4` `x=tan^-1(8/15) and y = tan^-1(3/4)->(2)` From (1) and (2),`L.H.S = tan^-1(8/15)+tan^-1(3/4)` We know, `tan^-1x+tan-^-1y = tan^-1((x+y)/(1-xy))` So,`=tan^-1(8/15+3/4)/(1-(8/15)*(3/4))` `=tan^-1(77/36) = R.H.S.`

Discussion

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