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Solve for `x :``2tan^(-1)(sinx)=tan^(-1)(2secx), x!=pi/2` |
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Answer» `2tan^-1(sinx) = tan^-1(2secx)` Applying `tan` both sides, `=> tan(2tan^-1(sinx)) = tan(tan^-1(2secx))` `=>(2tan(tan^-1(sinx)))/(1-tan^2(tan^-1(sinx))) = 2secx` `=>(2sinx)/(1-sin^2x) = 2secx` `=>sinx/cos^2x = 1/cosx` `=>six/cosx = 1` `=>tanx = 1` `=>x = npi+pi/4` |
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