How do you prove that $\frac{cos 3 θ}{sin θ} + \frac{sin 3 θ}{cos θ} = 2 cot 2 θ$ $(cos3theta)/sintheta +(sin3theta)/costheta = 2cot2theta$ ?

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Answer 1 · 2018-04-19T16:23:12

Please see below.

$\frac{cos 3 θ}{sin θ} + \frac{sin 3 θ}{cos θ}$ $(cos3theta)/sintheta+(sin3theta)/costheta$

= $\frac{cos 3 θ cos θ + sin 3 θ sin θ}{sin θ cos θ}$ $(cos3thetacostheta+sin3thetasintheta)/(sinthetacostheta)$

= $\frac{2 cos (3 θ - θ)}{2 sin θ cos θ}$ $(2cos(3theta-theta))/(2sinthetacostheta)$

= $\frac{2 cos 2 θ}{sin 2 θ}$ $(2cos2theta)/(sin2theta)$

= $2 cot 2 θ$ $2cot2theta$

How do you prove that cos3θsinθ+sin3θcosθ=2cot2θ(cos3theta)/sintheta +(sin3theta)/costheta = 2cot2theta?