Question

2sin²3π/4+2cos²3π/4-2tan²3π/4

Answer 1

Answer on Question #70157 – Math – Trigonometry

Question

$$2 \sin^2 \left(\frac{3\pi}{4}\right) + 2 \cos^2 \left(\frac{3\pi}{4}\right) - 2 \tan^2 \left(\frac{3\pi}{4}\right)$$

Solution

The Pythagorean Identity is given by

$$\sin^2 u + \cos^2 u = 1$$

We have that

$$\tan(3\pi/4) = 1.$$

Then

$$\begin{aligned} 2 \sin^2 \left(\frac{3\pi}{4}\right) + 2 \cos^2 \left(\frac{3\pi}{4}\right) - 2 \tan^2 \left(\frac{3\pi}{4}\right) &= \\ 2 \left(\sin^2 \left(\frac{3\pi}{4}\right) + \cos^2 \left(\frac{3\pi}{4}\right)\right) - 2 \tan^2 \left(\frac{3\pi}{4}\right) &= \\ 2 \times 1 - 2 \times 1^2 &= 0. \end{aligned}$$

Answer: 0.

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