If `alpha, beta and gamma` are the three angles with `alpha = 2tan^(-1)(sqrt2-1); beta = 3sin^(-1)(1/sqrt2)+sin^(-1)(-1/2)` and `gamma = cos^(-1)(1/3),` then

Options

A. `alpha glt beta lt y`
B. `alpha lt gamma lt beta`
C. `beta lt gamma lt alpha`
D. `gamma lt beta lt alpha`

Explanation

To solve the problem step by step, we need to evaluate the angles \( \alpha \), \( \beta \), and \( \gamma \) given in the question.

### Step 1: Evaluate \( \alpha \)
Given:
\[ \alpha = 2 \tan^{-1}(\sqrt{2} - 1) \]
Using the double angle formula for tangent:
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