Question 181996
a)obtain an expression for cos 2x in terms of sin^2 x
cos(A+B) = cos A cos B - sin A sin B
Let A = x and B = x

cos(x+x) = cos x cos x - sin x sin x
cos(2x) = cos^2(x) - sin^2(x)
We know sin^2(x) + cos^2(x) = 1
So
cos(2x) = cos^2(x) - sin^2(x)
cos(2x) = (1-sin^2(x)) - sin^2(x)
cos(2x) = 1-2sin^2(x)

Use this URL to verify your answers --> http://www.sosmath.com/trig/Trig5/trig5/trig5.html

b) is a lot like a. You can do that one