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

The general solution for solvefor x,2sin^2(x)+cos(x)=1 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin

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

solve for

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 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) = - \frac{1}{2}, cos (x) = 1

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

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

400 = 812.25 + 400 - 1140 cos (a)

3 cos (θ) = sin (θ)

- 4 cos^{(2)} (x) + 42 sin (x) + 6 = 0

3 tan^{2} (x) - 10 tan (x) + 7 = 0

What is the general solution for solvefor x,2sin^2(x)+cos(x)=1 ?
The general solution for solvefor x,2sin^2(x)+cos(x)=1 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin