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

The general solution for 2sin^2(x)=3cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Subtract

3 cos (x)

from both sides

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

Rewrite using trig identities

(1 - cos^{2} (x)) \cdot 2 - 3 cos (x) = 0

Solve by substitution

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

cos (x) = - 2 :

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

5 cos (θ) + 3 = 3 cos (θ) + 5

6 sec^{2} (x) - 8 = 0

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

tan (3 x) = 1, 0 \leq x \leq 2 π

sec^{2} (θ) - 9 sec (θ) + 20 = 0

What is the general solution for 2sin^2(x)=3cos(x) ?
The general solution for 2sin^2(x)=3cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin