prove that tan4x=4tanx(1-tan^2x)÷1-6tan^2x+tan^4x

1.	prove that tan4x=4tanx(1-tan^2x)÷1-6tan^2x+tan^4x
Answer» LHS = tan4x = tan(2x + 2x) use, the formula, tan(A + B) = (tanA+tanB)/(1-tanA.tanB) = (tan2x + tan2x)/(1-tan2x.tan2x) =2tan2x/(1-tan²2x) again, use the formula, tan2A = 2tanA/(1-tan²A) = 2{2tanx/(1-tan²x)}/[1-{2tanx/(1-tan²x)}²]=4tanx.(1-tan²x)²/(1-tan²x)(1+tan⁴x-2tan²x-4tan²x)=4tanx.(1-tan²x)/(1-6tan²x+tan⁴x) = RHS

Answer»

LHS = tan4x = tan(2x + 2x) use, the formula, tan(A + B) = (tanA+tanB)/(1-tanA.tanB)

= (tan2x + tan2x)/(1-tan2x.tan2x) =2tan2x/(1-tan²2x)

again, use the formula, tan2A = 2tanA/(1-tan²A)

= 2{2tanx/(1-tan²x)}/[1-{2tanx/(1-tan²x)}²]=4tanx.(1-tan²x)²/(1-tan²x)(1+tan⁴x-2tan²x-4tan²x)=4tanx.(1-tan²x)/(1-6tan²x+tan⁴x) = RHS

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