What is the general solution for 3sin(x)+3=2cos^2(x) ?

The general solution for 3sin(x)+3=2cos^2(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x=(3pi)/2+2pin

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3sin(x)+3=2cos^2(x)

3 sin (x) + 3 = 2 cos^{2} (x)

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

3 sin (x) + 3 = 2 cos^{2} (x)

Subtract

2 cos^{2} (x)

from both sides

3 sin (x) + 3 - 2 cos^{2} (x) = 0

Rewrite using trig identities

1 + 2 sin^{2} (x) + 3 sin (x) = 0

Solve by substitution

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

0 = 1 + 2 cos (θ)

1 - sin (x) = 1 + cos (x)

3 cos (2 x) - 7 cos (x) + 5 = 0

6 cos (x) + 3 = 0

What is the general solution for 3sin(x)+3=2cos^2(x) ?
The general solution for 3sin(x)+3=2cos^2(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x=(3pi)/2+2pin