trigonometry?

Question

Using exact values, verify that
Cos 60* = 1-2 Sin2 30*

With the work please

Answer 1

I assume the asterisks are supposed to be degree signs.

1 - 2(sin^2 (30)) =
1 - 2(1/2)^2 =
1 - 2/4 =
1/2 =
cos(60)

Answer 2

In a triangle of a angles 30°,60° and 90° , the following applies:-
-------30°------60°
sin---1/2------√3/2
cos √3/2------1/2

LHS = cos 60° = 1/2
RHS = 1 - 2.(1/2)² = 1 - 2/4 = 1/2

LHS = RHS

Answer 3

if you need to use triangles in your work, then draw a 30*,60*,90* triangle. The length of the hypotenuse (the longest leg) is 2 and the shortest leg is 1, the left over leg is sqrt(3).

now realize that sin = opposite leg/hyp and cos = adjacent leg/hyp

Answer 4

cos 60 = 1 - 2sin^2(30)

cos60 = 1/2
sin(30) = 1/2

1/2 = 1 - 2(1/2)^2

1/2 = 1 - 2(1/4)

1/2 = 1 - 1/2

1/2 = 1/2