Question

Considering only the values of sec²θcos(2θ) for the values of θ where it is defined sec²θ cos (2θ )= ?? Choose the correct answer from the options below:

A. 2sin²θ−tan2θ
B. csc²θ−2
C. 2−sec²θ
D. 2cotθ

Answer 1

The value of sec²θ cos(2θ) simplifies to 2 - sec²θ.

Step-by-step explanation:

To solve the equation sec²θ cos(2θ), we need to simplify the expression. We know that sec²θ = 1/cos²θ. So, substituting this into the equation, we get (1/cos²θ) cos(2θ). We can simplify further by using the double-angle identity, cos(2θ) = 2cos²θ - 1. Substituting this back into the equation, we get 1/(cos²θ) (2cos²θ - 1). This simplifies to 2 - sec²θ. Therefore, the correct answer is option C, 2 - sec²θ.