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

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

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

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

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

Solution steps

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

Subtract

cos (x)

from both sides

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

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

cot^{2} (x) = 1 - csc (x)

2 sin^{2} (θ) + 9 sin (θ) - 5 = 0

sin (x) tan (x) - sin (x) = 0

sinh (x) = \frac{15}{8}

(2 cos (x) - 1) (2 sin (x) - 3) = 0

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