Question

The greyed letters are the question. The blackened letters is the solution. How do I get there?

Answer 1

sin²θ

Explanation:

* trig identities are sin²θ + cos²θ = 1, sin²θ = 1 - cos²θ.

tan²θ = sin²θ/cos²θ.

sec²θ = 1/cos²θ.

Now we can begin to work it out.

(sec²θ - 1) / (1 + tan²θ)

Simplify sec and tan

((1/cos²θ) - 1) / (1 + (sin²θ/cos²θ))

now multiply every term by cos²θ

((cos²θ/cos²θ) - cos²θ) / ((cos²θ + sin²θ))

= (1 - cos²θ) / 1

= 1 - cos²θ

= sin²θ