Now write in terms of sine and cosine:
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- = \cos^2 x + 2\cos x \sec x + \sec^2 x + \sin^2 x + 2\sin x \csc x + \csc^2 x
- Since $ \cos x \sec x = 1 $, $ \sin x \csc x = 1 $, and $ \cos^2 x + \sin^2 x = 1 $, we get:
- = 1 + 2(1) + \sec^2 x + 2(1) + \csc^2 x = 1 + 2 + 2 + \sec^2 x + \csc^2 x = 5 + \sec^2 x + \csc^2 x
- \sec^2 x = \frac{1}{\cos^2 x}, \quad \csc^2 x = \frac{1}{\sin^2 x}
- \Rightarrow \text{Expression} = 5 + \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x}
- Use identity:
