Answer:
cos(2x) = 2cos²(x)-1
Step-by-step 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).
