Prove 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 term step by step.

### Step 1: Evaluate \( \sin\left(\frac{3\pi}{4}\right) \)
The angle \( \frac{3\pi}{4} \) is in the second quadrant. In the second quadrant, sine is positive.
\[ \sin\left(\frac{3\pi}{4}\right) = \sin\left(\pi - \frac{\pi}{4}\right) = \sin\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} \]

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