What is the general solution for 5sin(x)-4=2cos(2x) ?

The general solution for 5sin(x)-4=2cos(2x) is x=0.84806…+2pin,x=pi-0.84806…+2pin

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5sin(x)-4=2cos(2x)

5 sin (x) - 4 = 2 cos (2 x)

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Solution steps

5 sin (x) - 4 = 2 cos (2 x)

Subtract

2 cos (2 x)

from both sides

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

Rewrite using trig identities

- 6 + 4 sin^{2} (x) + 5 sin (x) = 0

Solve by substitution

sin (x) = \frac{3}{4}, sin (x) = - 2

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

sin (x) = - 2 :

No Solution

Combine all the solutions

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

Show solutions in decimal form

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

csc (x) + cot (x) = 0

cos^{2} (θ) - sin^{2} (θ) = 0

7 = 4 sin (\frac{π}{2} (x - 2)) + 5

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

503 = 100 \cdot \frac{cos ( x )}{sin ( x )}

What is the general solution for 5sin(x)-4=2cos(2x) ?
The general solution for 5sin(x)-4=2cos(2x) is x=0.84806…+2pin,x=pi-0.84806…+2pin