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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Rewrite using trig identities

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

Move

1

to the right side

2 sin^{2} (x) = 0

Divide both sides by

2

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

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

5 sin (1.75 x) = 1.4

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