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

The general solution for 2sin^2(x)-cos(x)=1 is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = - 1, cos (x) = \frac{1}{2}

cos (x) = - 1 : x = π + 2 πn

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 sin (2 θ) = 1

sin (\frac{π}{8})

csc (\frac{3 π}{4})

cos (2)

sin^{2} (θ) (1 + cot^{2} (θ)) = 1

What is the general solution for 2sin^2(x)-cos(x)=1 ?
The general solution for 2sin^2(x)-cos(x)=1 is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin