If `a,b,c inR` then prove that `sec^2theta=(bc+ca+ab)/(a^2+b^2+c^2)`only if a = b = c.

Explanation

To prove that \( \sec^2 \theta = \frac{bc + ca + ab}{a^2 + b^2 + c^2} \) only if \( a = b = c \), we will follow these steps:

### Step 1: Start with the given equation
We have:
\[ \sec^2 \theta = \frac{bc + ca + ab}{a^2 + b^2 + c^2} \]
Since \( \sec^2 \theta \geq 1 \) for all angles \( \theta \), we can write:
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