Question

Evaluate 1-2cos²25/1-2sin²65

Answer 1

Answer to Question #88536 – Math – Trigonometry

Question

Evaluate $(1 - 2\cos^2 25{}^\circ) / (1 - 2\sin^2 65{}^\circ)$

Solution

For the given problem, we first obtain the relation between the given sine and cosine angles. This has been shown below:

$$\begin{array}{l} \cos 25{}^\circ = \cos (90{}^\circ - 65{}^\circ) = \sin 65{}^\circ \\ \Rightarrow \cos 25{}^\circ = \sin 65{}^\circ \\ \Rightarrow \cos^2 25{}^\circ = \sin^2 65{}^\circ \\ \end{array}$$

So, now putting this relation into the main given expression, we get:

$$\begin{array}{l} \frac{(1 - 2\cos^2 25{}^\circ)}{(1 - 2\sin^2 65{}^\circ)} \\ = \frac{(1 - 2\sin^2 65{}^\circ)}{(1 - 2\sin^2 65{}^\circ)} \\ = 1 \\ \end{array}$$

Answer: 1.

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