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

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

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

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

Subtract

2 cos^{2} (x)

from both sides

3 + 3 sin (x) - 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

(cot (θ) + 1) (csc (θ) - \frac{1}{2}) = 0

tan^{2} (x) = 1 + sec^{2} (x)

cos (x) = \frac{50}{86}

cos (θ) = 1.1111111

sin (5 θ) - 17 = - 18

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