What is the general solution for cos(x)sin(x)-cos(x)=0 ?

The general solution for cos(x)sin(x)-cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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

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

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

Solution steps

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

Factor

cos (x) sin (x) - cos (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

sin^{2} (θ) = sin (θ)

(7 sin (2 x) + 7 cos (2 x))^{2} = 49

- 1 - tan (x) = sec (x)

5 cos (θ) + 4 = 0

2 sin^{2} (2 θ) = - 1 + 3 sin (2 θ)

What is the general solution for cos(x)sin(x)-cos(x)=0 ?
The general solution for cos(x)sin(x)-cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin