Prove that sec θ − cos θ = sin θ tan θ . - HSC - SSCE Mathematics Advanced - Question 19 - 2020 - Paper 1

Using the Pythagorean identity, we know that:

$$sin^2 θ + cos^2 θ = 1 \implies 1 − cos^2 θ = sin^2 θ$$

Substituting this back into our equation:

$$= \frac{sin^2 θ}{cos θ}$$

Recognizing that $tan θ = \frac{sin θ}{cos θ}$, we can rewrite:

$$= sin θ \cdot \frac{sin θ}{cos θ} = sin θ tan θ$$

Thus, the left-hand side equals the right-hand side (RHS), confirming:

LHS = RHS$$