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

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

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

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

x = πn, x = \frac{π}{2} + πn

Solution steps

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

Subtract

2 sin (2 x)

from both sides

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

Rewrite using trig identities

- \frac{3 sin ( 2 x )}{2} = 0

Multiply both sides by

2

- 3 sin (2 x) = 0

Divide both sides by

- 3

sin (2 x) = 0

General solutions for

sin (2 x) = 0

2 x = 0 + 2 πn, 2 x = π + 2 πn

Solve

2 x = 0 + 2 πn : x = πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

n, sin (x) + sin (13 \frac{n}{2} - x) = 1

5 cos^{2} (a) - 2 sin (a) - 2 = 0

tan^{2} (a) = \frac{( 2 tan ( a ) )}{( 1 - tan ^{2} ( a ) )}

12 cos^{2} (x) - 6 = sin (x)

cos^{2} (a) = \frac{2}{3}

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