Proved that `2sin^2``(3pi)/4``+2cos^2``pi/4``+2sec^2``pi/3=10`

Explanation

To prove that \( 2\sin^2\left(\frac{3\pi}{4}\right) + 2\cos^2\left(\frac{\pi}{4}\right) + 2\sec^2\left(\frac{\pi}{3}\right) = 10 \), we will evaluate each trigonometric function step by step.

### Step 1: Evaluate \( \sin\left(\frac{3\pi}{4}\right) \)

Using the identity:
\[ \sin\left(\frac{3\pi}{4}\right) = \sin\left(\pi - \frac{\pi}{4}\right) = \sin\left(\frac{\pi}{4}\right) \]
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