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Question

Prove that: sin1(35)+cos1(1213)=sin1(5665).

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Solution

Let cos1(1213)=x
1213=cosx
sinx=513
Let sin1(35)=y
35=siny
cosy=45
We know that, sin(x+y)=sinxcosy+cosxsiny
sin(x+y)=513×45+1213×35
sin(x+y)=5665
x+y=sin1(5665)
cos1(1213)+sin1(35)=sin1(5665)
Hence proved.

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