Simplify the expression by using a double-angle formula.

Question

cos^2 34 degree - sin 34 degree

Answer 1

I assume your problem is cos²(34°)-sin²(34°):

cos(2θ) = cos²θ-sin²θ

cos(2·34°) = cos²(34°)-sin²(34°)

cos(68°) = cos²(34°)-sin²(34°)

Therefore, cos(68°) is the correct answer. You can also use sin(22°) because of the co-function identity.

Hope this helped!

Answer 2

double angle formulas are:

cos2x = cos^2(x) - sin^2(x) = 2cos^2(x)-1 = 1 -2sin^2(x)

and

sin2x = 2sinxcosx

cos68 = cos^2(34) -sin^2(34)

= 2cos^2(34)-1

=1-2sin^2(34)

sin34 = 2sin17cos17