InterviewSolution
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InterviewSolution
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2tan xProve that tan 2x =1-tan x |
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Answer» tan(2x) = (2 tan x) / (1 - tan²x) Take the LHS.tan(2x) = tan x = sin x / cos x.sin(2x) / cos(2x) = sin 2A = 2 sin A cos A.2 sin x cos x / cos(2x) = cos 2A = cos²A - sin²A.2 sin x cos x / (cos²x - sin²x) = Divide the numerator and denominator by cos²x.(2 sin x cos x / cos²x) / [(cos²x - sin²x) / cos²x] =[2 sin x(1) / cos x] / [(cos²x / cos²x) - (sin²x / cos²x)] =[2(sin x / cos x)] / [1 - (sin²x / cos²x)] = t tan x = sin x / cos x.(2 tan x) / [1 - (sin²x / cos²x)] = tan²x = sin²x / cos²x.(2 tan x) / (1 - tan²x) =RHS |
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