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

The general solution for 2cos^2(x)+3sin(-x)-3=0 is x=(3pi)/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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

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

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 = 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

12 cos (\frac{x}{3}) = 0

x, y^{4} + 2 y + 1 = sin (x)

cos (2 x) = \frac{( 6 k - 9 )}{9}

csc (x) = 1 + cot (x)

6 sin^{2} (x) = 5 sin (x)

What is the general solution for 2cos^2(x)+3sin(-x)-3=0 ?
The general solution for 2cos^2(x)+3sin(-x)-3=0 is x=(3pi)/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin