What is the general solution for 2cos^2(x)-3sin(x)=0 ?

The general solution for 2cos^2(x)-3sin(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = - 2 :

No Solution

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

3 cos (x) = 1 + cos (x)

0 = 1 + 2 sin (x)

(cot (θ) + 1) (csc (θ) + 1) = 0

3 sec (x) csc (x) = 6 csc (x)

cos (2 x) + 6 sin^{2} (x) = 4

What is the general solution for 2cos^2(x)-3sin(x)=0 ?
The general solution for 2cos^2(x)-3sin(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin