What is the general solution for sin^2(x)-2cos^2(x)=1 ?

The general solution for sin^2(x)-2cos^2(x)=1 is x= pi/2+2pin,x=(3pi)/2+2pin

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sin^2(x)-2cos^2(x)=1

sin^{2} (x) - 2 cos^{2} (x) = 1

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

sin^{2} (x) - 2 cos^{2} (x) = 1

Subtract

1

from both sides

sin^{2} (x) - 2 cos^{2} (x) - 1 = 0

Rewrite using trig identities

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

Divide both sides by

- 3

cos (x) = 0

General solutions for

cos (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) = - \frac{12}{13}

2 sin^{2} (x) + 7 sin (x) - 4 = 0

cos (\frac{5 π}{4} + x) + sin (\frac{5 π}{4} - x) = 0

cos (2 x) + sin (2 x) = 1

θ, sin (θ) = \frac{1}{2}

What is the general solution for sin^2(x)-2cos^2(x)=1 ?
The general solution for sin^2(x)-2cos^2(x)=1 is x= pi/2+2pin,x=(3pi)/2+2pin