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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

2 sin (x)

from both sides

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

Factor

2 sin (x) cos (x) - 2 sin (x) : 2 sin (x) (cos (x) - 1)

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

Solving each part separately

sin (x) = 0 or cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

sin^{2} (θ) = 3 - 2 cos^{2} (θ)

sin (x) = \frac{7}{5}

csc (3 x) = 2

2 cos (x) + sec (x) = 3

cos^{2} (2 x) = 0

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