Question

cosec2A-cot2A

Answer 1

Answer on Question #52821 – Math – Trigonometry

$$cosec(2A) - \cot(2A)$$

Solution

$$\begin{aligned} & \text{cosec}(2A) - \cot(2A) = \frac{1}{\sin(2A)} - \frac{\cos(2A)}{\sin(2A)} = \frac{1 - \cos(2A)}{\sin(2A)} = \\ & = \frac{1 - \cos^2(A) + \sin^2(A)}{\sin(2A)} = \frac{\sin^2(A) + \sin^2(A)}{2 \sin(A) \cos(A)} = \frac{2 \sin^2(A)}{2 \sin(A) \cos(A)} = \\ & = \frac{\sin(A)}{\cos(A)} = \tan(A) \\ & \quad \text{cosec}(2A) - \cot(2A) = \tan(A) \end{aligned}$$

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