Prove the trigonometric identity? $tanx(1-cot^2x)+cotx(1-tan^2x)=0$

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Prove the trigonometric identity? $tanx(1-cot^2x)+cotx(1-tan^2x)=0$

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Answer 1 · 2016-07-17T03:41:33

Prove trig identity.

Explanation:

Replace in the equation $tan x = (sin x)/(cos x)$ , and $cot x = (cos x)/(sin x)$
$(sin x)/(cos x)(1 - (cos^2 x)/(sin^2 x)) + (cos x)/(sin x) (1 - sin^2 x/(cos^2 x)) =$
$(sin x)/(cos x) - (cos x)/(sin x) + (cos x)/(sin x) - (sin x)/(cos x) = 0$ OK

Answer 2 · 2016-07-17T08:03:53

Applying identity $tanxcotx=1$

$LHS=tanx(1-cot^2x)+cotx(1-tan^2x)$

$=tanx-tanxcot^2x+cotx-cotxtan^2x$

$=tanx-1*cotx+cotx-1*tanx$

$=0=RHS$

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Prove the trigonometric identity? $tanx(1-cot^2x)+cotx(1-tan^2x)=0$

2 Answers

Explanation:

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Science

Math

Humanities

... and beyond

Prove the trigonometric identity? tanx(1-cot^2x)+cotx(1-tan^2x)=0tanx(1-cot^2x)+cotx(1-tan^2x)=0

2 Answers

Explanation:

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Prove the trigonometric identity? $tanx(1-cot^2x)+cotx(1-tan^2x)=0$