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

The general solution for cos^2(x)+3sin(-x)-2=0 is x=-0.39192…+2pin,x=pi+0.39192…+2pin

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

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

x = - 0.39192 \dots + 2 πn, x = π + 0.39192 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - \frac{3 + 5}{2}, sin (x) = - \frac{3 - 5}{2}

sin (x) = - \frac{3 + 5}{2} :

No Solution

sin (x) = - \frac{3 - 5}{2} : x = arcsin (- \frac{3 - 5}{2}) + 2 πn, x = π + arcsin (\frac{3 - 5}{2}) + 2 πn

Combine all the solutions

x = arcsin (- \frac{3 - 5}{2}) + 2 πn, x = π + arcsin (\frac{3 - 5}{2}) + 2 πn

Show solutions in decimal form

x = - 0.39192 \dots + 2 πn, x = π + 0.39192 \dots + 2 πn

cos (x) = - 1, 0 < x < 2 π

\frac{1}{1 + cos ( x )} + \frac{1}{1 - cos ( x )} = 32

sin^{2} (x) = 14

sin (2 x) \cdot cos (3 x) = 0

sin^{2} (x) = - 3

What is the general solution for cos^2(x)+3sin(-x)-2=0 ?
The general solution for cos^2(x)+3sin(-x)-2=0 is x=-0.39192…+2pin,x=pi+0.39192…+2pin