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

The general solution for cos(2x)-3sin(-x)+2=0 is x=-0.75617…+2pin,x=pi+0.75617…+2pin

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

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

x = - 0.75617 \dots + 2 πn, x = π + 0.75617 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - \frac{- 3 + 33}{4}, sin (x) = \frac{3 + 33}{4}

sin (x) = - \frac{- 3 + 33}{4} : x = arcsin (- \frac{- 3 + 33}{4}) + 2 πn, x = π + arcsin (\frac{- 3 + 33}{4}) + 2 πn

sin (x) = \frac{3 + 33}{4} :

No Solution

Combine all the solutions

x = arcsin (- \frac{- 3 + 33}{4}) + 2 πn, x = π + arcsin (\frac{- 3 + 33}{4}) + 2 πn

Show solutions in decimal form

x = - 0.75617 \dots + 2 πn, x = π + 0.75617 \dots + 2 πn

0 = - sin (8 x) + sin (6 x)

3 tan (x) sin (x) - 3 sin (x) = 0

cot^{4} (x) - 3 cot^{2} (x) + 1 = 0

\frac{cos ( - 3 0 ^{\circ} + x )}{cos ( 3 0 ^{\circ} + x )} = \frac{1835}{726}

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

What is the general solution for cos(2x)-3sin(-x)+2=0 ?
The general solution for cos(2x)-3sin(-x)+2=0 is x=-0.75617…+2pin,x=pi+0.75617…+2pin