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

The general solution for 2sin^2(x)+3cos(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = 2 :

No Solution

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos^{2} (θ) + sin (θ) = 1

sin (x) = \frac{2}{2}

2 sin (x) - 1 = 0

cos (x) + sin (x) = 0

cos (x) + sin (x) tan (x) = 2

What is the general solution for 2sin^2(x)+3cos(x)=0 ?
The general solution for 2sin^2(x)+3cos(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin