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

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

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

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

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

Solution steps

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

Subtract

3

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

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

Combine all the solutions

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

14 cos (θ) - 5 = 5 cos (θ) - 5

- 4 sin (2 θ) = 5 cos (2 θ)

tan (A) = \frac{3}{4}

2 sin (3 x) + 1 = 0

3 sin (θ) = cos (θ), 0 \leq θ \leq 2 π

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