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Prove that `sin^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))` |
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Answer» Here, we will use, `sin^-1x+sin^-1y = sin^-1(xsqrt(1-y^2)+ysqrt(1-x^2))` `L.H.S. = sin^-1(8/17)+sin^-1(3/5)` `=sin^-1(8/17sqrt(1-(3/5)^2)+3/5sqrt(1-(8/17)^2))` `=sin^-1(8/17(4/5)+3/5(15/17))` `=sin^-1(32/85+45/85)` `=sin^-1(77/85)` `=cos^-1(sqrt(1-(77/85)^2))` `=cos^-1(sqrt(1296/7225))` `=cos^-1(36/85) = R.H.S.` |
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