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Prove that:sin^(-1)(8/17)+sin^(-1)(3/5)=...

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

Text Solution

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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, ...
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