Prove the trig identity: Sec θ - Cos θ/Sec θ = Sin^2 θ

1. Start with the left-hand side (LHS):

\text{LHS} = \frac{\sec \theta - \cos \theta}{\sec \theta}

2. Rewrite the terms in terms of sine and cosine:

\sec \theta = \frac{1}{\cos \theta}

3. Substitute into the LHS:

\text{LHS} = \frac{\frac{1}{\cos \theta} - \cos \theta}{\frac{1}{\cos \theta}}

4. Simplify the expression inside the fraction:

= \frac{\frac{1 - \cos^2 \theta}{\cos \theta}}{\frac{1}{\cos \theta}}

5. Simplify further by multiplying by the reciprocal:

= (1 - \cos^2 \theta)

6. Substitute the Pythagorean identity:

= \sin^2 \theta

Hence, the identity is proven since:

\frac{\sec \theta - \cos \theta}{\sec \theta} = \sin^2 \theta

So, the right-hand side (RHS) and transformed LHS are equal.

This completes the proof of the identity.