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Asked by Ashwini Last Modified
Answer 
Let sin-1(3/5) = x and sin-1(8/17) = y
Therefore sinx = 3/5 and siny = 8/17
Now, cosx = √(1 - sin2x) = √(1 - (3/5)2) = √(1 - 9/25) = 4/5 and cosy = √(1 - sin2y) = √(1 - (8/17)2) = √(1 - 64/289) = 15/17
We have cos(x - y) = cosx cosy + sinx siny = 4/5 x 15/17 + 3/5 x 8/17 = 60/85 + 24/85 = 84/85 ⇒ x - y = cos-1(84/85) ⇒ sin-1(3/5) - sin-1(8/17) = cos-1(84/85)
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