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

The general solution for 2cos^2(x)+sin(x)=2 is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 0, sin (x) = \frac{1}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = 4

csc (x) = 3

2 - 8 cos^{2} (t) = 0

cos (θ) + 1 = 1

9 cos (x) tan (x) = - 8 tan (x)

What is the general solution for 2cos^2(x)+sin(x)=2 ?
The general solution for 2cos^2(x)+sin(x)=2 is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(5pi)/6+2pin