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

The general solution for 2sin(x)=2+cos(2x) is x=0.96645…+2pin,x=pi-0.96645…+2pin

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

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

x = 0.96645 \dots + 2 πn, x = π - 0.96645 \dots + 2 πn

Solution steps

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

Subtract

2 + cos (2 x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = \frac{- 1 + 7}{2}, sin (x) = - \frac{1 + 7}{2}

sin (x) = \frac{- 1 + 7}{2} : x = arcsin (\frac{- 1 + 7}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 7}{2}) + 2 πn

sin (x) = - \frac{1 + 7}{2} :

No Solution

Combine all the solutions

x = arcsin (\frac{- 1 + 7}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 7}{2}) + 2 πn

Show solutions in decimal form

x = 0.96645 \dots + 2 πn, x = π - 0.96645 \dots + 2 πn

sin (x) = \frac{- \frac{4}{3} 3}{\frac{8}{3} 3}

sec (a) = \frac{5}{4}

cot^{4} (x) - 9 = 0

0.5 \cdot sin (x) = 1 \cdot (645 \cdot 1 0^{- 9})

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

What is the general solution for 2sin(x)=2+cos(2x) ?
The general solution for 2sin(x)=2+cos(2x) is x=0.96645…+2pin,x=pi-0.96645…+2pin