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Question
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
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Solution
L.H.S. `sin^-1 8/17 + sin^-1 3/5`
Using `sin^-1x +sin^-1y sin^-1[xsqrt(1 - y^2) + ysqrt(1 - x^2)]`
`sin^-1 8/17 + sin^-1 3/5 = sin^-1[8/17* sqrt(1 - (3/5)^2) + 3/5 * sqrt(1 (8/1)^2)]`
= `sin^-1[8/17 * sqrt(1 9/25) + 3/5* sqrt(1 - 64/289)]`
= `sin^-1 [8/17 * sqrt(16/25) + 3/5* sqrt(225/289)]`
= `sin^-1 [8/17 * 4/5 +3/5 * 15/17]`
= `sin-1 [32/85 + 45/85]`
=`sin^-1 77/85` R.H.S.
Hence proved.
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