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

The general solution for 2sin(x)cos(x)=cos(2x) is x= pi/8+(pin)/2

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

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

x = \frac{π}{8} + \frac{πn}{2}

Solution steps

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

Subtract

cos (2 x)

from both sides

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

Rewrite using trig identities

- 1 + tan (2 x) = 0

Move

1

to the right side

tan (2 x) = 1

General solutions for

tan (2 x) = 1

2 x = \frac{π}{4} + πn

Solve

2 x = \frac{π}{4} + πn : x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

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

sin (θ) = \frac{0.3924}{cos ( θ )}

x, y = 3 sin (x)

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

cos (x) = \frac{32}{34.54}

What is the general solution for 2sin(x)cos(x)=cos(2x) ?
The general solution for 2sin(x)cos(x)=cos(2x) is x= pi/8+(pin)/2