Sin^2x-cos^2=Корень2/2

Применим формулу:

cos2α = cos∧2x - sin∧2x; - (cos∧2x - sin∧x) = - cos2α

- cos (2α) = √2/2

cos (2α) = - √2/2

2α = (+ -) arccos (√2/2) + 2πn, n∈Z

2α = (+ -) (π - π/4) + 2πn, n∈Z

2α = (+ -) (3π/4) + 2πn. n∈Z

α = (+ -) (3π/8) + πn, n∈Z