What is the general solution for sin^2(x)-3cos^2(x)=1 ?

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

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sin^2(x)-3cos^2(x)=1

sin^{2} (x) - 3 cos^{2} (x) = 1

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

Solution steps

sin^{2} (x) - 3 cos^{2} (x) = 1

Subtract

1

from both sides

sin^{2} (x) - 3 cos^{2} (x) - 1 = 0

Rewrite using trig identities

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

Divide both sides by

- 4

cos (x) = 0

General solutions for

cos (x) = 0

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

a, sin (arccos (x)) = 1 - x^{2}

7 cos (5 x) = 6

3 sin (x) = 3 tan (x)

3 cos (11 θ) = 0

cos (2 a) = - 1

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