Question

1. Choose the trig expression equal to the one below 2cos^2 x - 1

Answer 1

cos(2x) = 2cos²(x)-1

Explanation:

We know the trigonometry identity as follows :

cos(2x) = cos²(x) – sin²(x) ....(1)

Also, sin²(x)+cos²(x) = 1

or

sin²(x) = 1-cos²(x)

Put the value of sin²(x) in equation (1)

cos(2x) = cos²(x) – (1-cos²(x))

= cos²(x) –1+cos²(x)

cos(2x) = 2cos²(x)-1

Hence, 2cos²(x)-1 is equal to cos(2x).