What is the general solution for 4-4cos(2x)-3sin(x)=0 ?

The general solution for 4-4cos(2x)-3sin(x)=0 is x=0.38439…+2pin,x=pi-0.38439…+2pin,x=2pin,x=pi+2pin

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4-4cos(2x)-3sin(x)=0

4 - 4 cos (2 x) - 3 sin (x) = 0

x = 0.38439 \dots + 2 πn, x = π - 0.38439 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

4 - 4 cos (2 x) - 3 sin (x) = 0

Rewrite using trig identities

- 3 sin (x) + 8 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{3}{8}, sin (x) = 0

sin (x) = \frac{3}{8} : x = arcsin (\frac{3}{8}) + 2 πn, x = π - arcsin (\frac{3}{8}) + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = arcsin (\frac{3}{8}) + 2 πn, x = π - arcsin (\frac{3}{8}) + 2 πn, x = 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.38439 \dots + 2 πn, x = π - 0.38439 \dots + 2 πn, x = 2 πn, x = π + 2 πn

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

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

arctan (x) = arccos (\frac{3}{4})

tan^{2} (θ) + 7 tan (θ) + 9 = 0

x, cos (x) \cdot cos (y) = 0

What is the general solution for 4-4cos(2x)-3sin(x)=0 ?
The general solution for 4-4cos(2x)-3sin(x)=0 is x=0.38439…+2pin,x=pi-0.38439…+2pin,x=2pin,x=pi+2pin