What is the general solution for 2cos^2(x)=3(sin(x)+1) ?

The general solution for 2cos^2(x)=3(sin(x)+1) is x=(3pi)/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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2cos^2(x)=3(sin(x)+1)

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

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) + 1)

Subtract

3 (sin (x) + 1)

from both sides

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

cos^{2} (θ) = \frac{2 + 3}{4}

x, cos (x) = sin (x + y)

2 cos (5 x) = 9

- 5 cos (c) - 1 = 2 cos (c) + 3

3 tan (t) - cot (t) - 5 = 0

What is the general solution for 2cos^2(x)=3(sin(x)+1) ?
The general solution for 2cos^2(x)=3(sin(x)+1) is x=(3pi)/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin