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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

sin (θ) = \frac{1}{4}, 0 < θ < \frac{π}{2}

sin (2 θ) = \frac{1.35 \cdot 10}{( 38 ) ^{2}}

- 2 = \frac{16}{π} cos (4 \cdot x)

- (\frac{1}{2})^{2} + cos (θ^{2}) = 1

0 = 2 cos (2 θ)

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