Question

prove that
sin inverse $\frac{3}{5}$+sin inverse $\frac{-8}{17}$= cos inverse $\frac{36}{85}$

Answer 1

Put $sin^{-1}3/5$ = A and $sin^{-1} 8/17$= B,

we get sin A =  3/5 and Sin B= 8/17

Now, convert these values to cos.

using the formula  $Cos^{2}x=1-sin^{2}x$

we get,Cos  A = 4/5 and Cos B=15/17,

Use the formula Cos ( A+B) = CosACosB - SinASinB

we get Cos(A+B)=4/7 * 15/17 - 3/5 *8/17

Cos (A+B)= 36/85

Or A+B =$Cos^{-1} 36/85$,

Substitute values of A and B,

$sin^{-1}3/5$ - $sin^{-1}8/17$= $cos^{-1}36/85$

Answer 2

I hope that you got your required answer
Well you will get cos inverse 36/85 if sin inverse 3/5 - sin inverse -8/17 is present
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