What is the general solution for 2cos^2(x)-2sin^2(x)=0 ?

The general solution for 2cos^2(x)-2sin^2(x)=0 is x=(3pi)/4+pin,x= pi/4+pin

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2cos^2(x)-2sin^2(x)=0

2 cos^{2} (x) - 2 sin^{2} (x) = 0

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

Solution steps

2 cos^{2} (x) - 2 sin^{2} (x) = 0

Factor

2 cos^{2} (x) - 2 sin^{2} (x) : 2 (cos (x) + sin (x)) (cos (x) - sin (x))

2 (cos (x) + sin (x)) (cos (x) - sin (x)) = 0

Solving each part separately

cos (x) + sin (x) = 0 or cos (x) - sin (x) = 0

cos (x) + sin (x) = 0 : x = \frac{3 π}{4} + πn

cos (x) - sin (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

csc^{2} (θ) + 5 = 7 - csc (θ)

3 tan^{2} (\frac{x}{3}) - 1 = 0

cos (x) = \frac{7}{10}

2 cos (2 x) + 3 = 2

2 cos (x) = sec (x)

What is the general solution for 2cos^2(x)-2sin^2(x)=0 ?
The general solution for 2cos^2(x)-2sin^2(x)=0 is x=(3pi)/4+pin,x= pi/4+pin