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

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

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

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

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

Solution steps

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

3 \cdot sin (x) = cos (x)

sin^{22} (x) sin^{3} (x) + 6 = 18

d^{2} + 4 d + 4 = sin (x)

8 cos (a) - 15 sin (a) = 0

tan (t) = \frac{3}{tan ( t )}

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