Changing to sinθ and cosθ , we get θ #160; 2θ #160; =cosθ #160; #160; sinθ #160; #160; cos 2θ #160; #160; sin 2θ #160; ...

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Trigonometric Ratios of Multiples of an Angle

Prove: θ - ...

Question

Prove: $cot θ - cot 2 θ = c o sec 2 θ$

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Solution

Changing to $sin θ$ and $cos θ$ , we get
$cot θ - cot 2 θ = \frac{cos θ}{sin θ} - \frac{cos 2 θ}{sin 2 θ} = \frac{sin 2 θ cos θ - cos 2 θ sin θ}{sin θ sin 2 θ} = \frac{sin (2 θ - θ)}{sin θ sin 2 θ} = c o sec 2 θ$

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