Question

How do I get this answer?

Answer 1

Answer:

Step-by-step explanation:

Several trig identities are involved in the proof of this. This is the order in which they are used.

• cos(2x) = cos²(x) -sin²(x)
• cos²(x) +sin²(x) = 1
• cos(x) = 1/sec(x)

Proof

Starting with the left side, we can transform it into the right side.

  $2\cos(2x)=2(\cos^2(x)-\sin^2(x)) = 2(\cos^2(x)-(1-\cos^2(x)))\\\\=2(2\cos^2(x)-1)=2\left(\dfrac{2}{\sec^2(x)}-\dfrac{\sec^2(x)}{\sec^2(x)}\right)\\\\=\boxed{\dfrac{4-2\sec^2(x)}{\sec^2(x)}}$