What is the general solution for -2sin(x)+cos(2x)=1 ?

The general solution for -2sin(x)+cos(2x)=1 is x=(3pi)/2+2pin,x=2pin,x=pi+2pin

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-2sin(x)+cos(2x)=1

- 2 sin (x) + cos (2 x) = 1

x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

- 2 sin (x) + cos (2 x) = 1

Subtract

1

from both sides

- 2 sin (x) + cos (2 x) - 1 = 0

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 1, sin (x) = 0

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn

4 cos (x) tan (x) - 3 tan (x) = 0

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

sin (x) = 2 cos (x)

sec (x) tan (x) = 0

2 cos (x) + 1 = 3

What is the general solution for -2sin(x)+cos(2x)=1 ?
The general solution for -2sin(x)+cos(2x)=1 is x=(3pi)/2+2pin,x=2pin,x=pi+2pin