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

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

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

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

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

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

- 1 + 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

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

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

cos (\frac{3 x - 7}{2}) = 0

3 tan^{2} (x) = \frac{8}{sin ^{2} ( x )}

sin^{2} (x) + sin^{22} (x) + sin^{23} (x) = 1

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