Question

Which of the following is equivalent to sec2θ−1sec2θ for all values of θ for which sec2θ−1sec2θ is defined?

Answer 1

Answer:

$2 sin^2 \theta$

Step-by-step explanation:

According to the scenario, the following information is given:

$= \frac{sec^2 \theta - 1 }{sec^2 \theta}$

$= (\frac{1}{\frac{cos^2\theta}{\frac{1}{cos^2\theta} }} - 1)$

$= 1 - cos^2\theta\\\\= 1 - (1 - 2 sin^2 \theta)\\\\= 2 sin^2 \theta$

Therefore for the given equation, the answer is $2 sin^2 \theta$