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

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

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

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

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

Solution steps

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

Subtract

1

from both sides

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

15 cos (x) - 5 = 4 cos (x)

sin (θ) + cos (θ) = \frac{2 + 3}{2}

x, arctan (\frac{1}{x}) = 8 0^{\circ}

2 sin (θ) cos (θ) + 2 sin (θ) + cos (θ) + 1 = 0

cos (x) - cos (2 x) = 0, 0 \leq x \leq 2 π

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