How do you verify $\frac{1 + cos 2 x}{sin 2 x} = cot x$ $(1+cos2x)/(sin2x) = cotx$ ?

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Answer 1 · 2015-07-03T19:53:56

Since

$cos 2 x = {cos}^{2} x - {sin}^{2} x = 1 - 2 {sin}^{2} x = 2 {cos}^{2} x - 1$ $cos2x=cos^2x-sin^2x=1-2sin^2x=2cos^2x-1$

and

$sin 2 x = 2 sin x cos x$ $sin2x=2sinxcosx$

then:

$\frac{1 + 2 {cos}^{2} x - 1}{2 sin x cos x} = cot x \Rightarrow$ $(1+2cos^2x-1)/(2sinxcosx)=cotxrArr$

$\frac{2 {cos}^{2} x}{2 sin x cos x} = cot x \Rightarrow$ $(2cos^2x)/(2sinxcosx)=cotxrArr$

$\frac{cos x}{sin x} = cot x \Rightarrow$ $cosx/sinx=cotxrArr$

$cot x = cot x$ $cotx=cotx$ .

How do you verify 1+cos2xsin2x=cotx(1+cos2x)/(sin2x) = cotx?