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

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

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

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

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

Solution steps

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

Subtract

cos^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 1, sin (x) = - 1

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

sin (2 θ) = \frac{1}{3}

cos^{2} (θ) = 1 - sin (θ)

1 sin (3 0^{\circ}) = 1.495 sin (x)

e^{2 c o s (x) - 1} = 1

csc (θ) = - \frac{37}{12}, \frac{3 π}{2} \leq θ \leq 2 π

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