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

Prove that `sin^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))`

Text Solution

Verified by Experts

Let `sin^(-1)(3/5)=theta`
`rArrsintheta=3/5`
`costheta=4/5`
`and sin^(-1)(8/17)=phi`
`rArrsinphi=8/17`
`rArr cosphi=15/17`

Now `cos(theta+phi)=costhetacosphi-sinthetasinphi`
`=4/5xx15/17-3/5xx8/17`
`=(60-24)/85`
`=36/85`
`rArrtheta+phi=cos^(-1)36/85`
`rArrsin^(-1)(3/5)+sin^(-1)(8/17)=cos^(-1)(36/85)`
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