How do I solve for the value of x in degrees given #cos^2(x) - sin^2(x) =sqrt3/2#?

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Answer 1 · 2018-02-21T23:42:29

Given: #cos^2(x) - sin^2(x) =sqrt3/2#

Use the identity #cos(2x) = cos^2(x)-sin^2(x)#:

#cos(2x) =sqrt3/2#

Use the inverse cosine function on both sides:

#2x =cos^-1(sqrt3/2)#

As we rotate around the unit circle, the first angle that corresponds to a cosine value of #sqrt3/2# is #30^@#

#2x =30^@#

Divide both sides by 2:

#x =15^@#