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

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

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

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

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

Subtract

2

from both sides

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 (2 x) + sin (4 x) = 0

sin (x) = 0.3

sin (3 θ) = 0

cot (x) - 1 = 0

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

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