How do you prove the identity $\frac{1 + cos 2 θ}{sin (2 θ)} = cot θ$ $(1+cos2theta)/sin(2theta)=cottheta$ ?

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Answer 1 · 2016-09-09T04:31:13

Prove identity

Use the trig identities:
$1 + cos 2 a = 2 {cos}^{2} a$ $1 + cos 2a = 2cos^2 a$
$sin 2 a = 2 sin a . cos a$ $sin 2a = 2sin a.cos a$

$P = \frac{2 {cos}^{2} t}{2 sin t . cos t} = \frac{cos t}{sin t} = cot t$ $P = (2cos^2 t)/(2sin t.cos t) = (cos t)/(sin t) = cot t$

How do you prove the identity 1+cos2θsin(2θ)=cotθ(1+cos2theta)/sin(2theta)=cottheta?