If `tanalpha=1/7,sinbeta=1/(sqrt(10)),` prove that`alpha+2beta=pi/4` , where `0

Explanation

To prove that \(\alpha + 2\beta = \frac{\pi}{4}\) given that \(\tan \alpha = \frac{1}{7}\) and \(\sin \beta = \frac{1}{\sqrt{10}}\), we can follow these steps:

### Step 1: Find \(\tan \beta\)
We know that:
\[ \sin \beta = \frac{1}{\sqrt{10}} \]
Using the Pythagorean identity, we can find \(\cos \beta\):
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