How do you solve $cos^2x - sin^2x=sqrt3/2$ ?

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Answer 1 · 2015-08-12T04:05:18

Solve $cos^2 x - sin^2 x = sqrt3/2$

General solution:
$x = npi +- pi/12, " " n in ZZ$

Use trig identity: $cos 2a = cos^2 a - sin^2 a$

$cos^2 x - sin^2 x = cos 2x = sqrt3/2$
$2x = +- pi/6$
$2x = 2npi +- pi/6, " " n in ZZ$

General solution:
$x = npi +- pi/12, " " n in ZZ$

How do you solve cos^2x - sin^2x=sqrt3/2cos^2x - sin^2x=sqrt3/2?