SOLUTION: The expression cos^2 40 degrees - sin^2 40 degrees has the same value as (1) sin 20 degrees (2) sin80 degrees (3) cos 80 degrees (4) cos 20 degrees .... I do not know how

Algebra ->  Trigonometry-basics -> SOLUTION: The expression cos^2 40 degrees - sin^2 40 degrees has the same value as (1) sin 20 degrees (2) sin80 degrees (3) cos 80 degrees (4) cos 20 degrees .... I do not know how       Log On


   

Question 609772: The expression cos^2 40 degrees - sin^2 40 degrees has the same value as
(1) sin 20 degrees (2) sin80 degrees (3) cos 80 degrees (4) cos 20 degrees
....
I do not know how to go about this question...all I know is this identity
sin^2 theta + cos^2 theta = 1, but I do not know how to apply it.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the identity cos^2(x) - sin^2(x) = cos(2x) to get


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

cos^2(40) - sin^2(40) = cos(2*40)

cos^2(40) - sin^2(40) = cos(80)
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