If `alpha, beta, gamma` are direction angles of a line l, then prove that
`cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`.
Hence, deduce that `sin^(2) alpha + sin^(2) beta + sin^(2) gamma = 2`.

Explanation

To prove that \( \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1 \) where \( \alpha, \beta, \gamma \) are the direction angles of a line \( l \), we can follow these steps:

### Step 1: Understanding Direction Angles
The direction angles \( \alpha, \beta, \gamma \) are the angles that the line makes with the positive x-axis, y-axis, and z-axis respectively. The cosine of these angles gives the direction cosines of the line.

### Step 2: Definition of Direction Cosines
Let \( l \) be a line in three-dimensional space. The direction cosines \( l, m, n \) corresponding to angles \( \alpha, \beta, \gamma \) are defined as:
\[
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