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

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

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

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

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

Solution steps

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

Factor

sin (x) cos (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

tan (x) = \frac{5}{2}

4 sin (x) cos (x) = 3

3 sin (x) + 4 cos (x) = 2

cot^{2} (x) - 6 cot (x) + 5 = 0, 0 \leq x \leq 2 π

9 tan (θ) + 13 = 2 tan (θ) + 6

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