What is the general solution for cos^2(x)-sin(x)cos(x)=0 ?

The general solution for cos^2(x)-sin(x)cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/4+pin

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

cos^{2} (x) - sin (x) cos (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{4} + πn

Solution steps

cos^{2} (x) - sin (x) cos (x) = 0

Factor

cos^{2} (x) - sin (x) cos (x) : cos (x) (cos (x) - sin (x))

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

Solving each part separately

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

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

cos (x) - sin (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{4} + πn

cos (θ) sin (θ) = 1

x, 4 sin (x) + 2 = 0

3 = - tan (x)

- tan^{2} (x) - 2 tan (x) - 1 = 0

sin (x) = \frac{4}{6 2}

What is the general solution for cos^2(x)-sin(x)cos(x)=0 ?
The general solution for cos^2(x)-sin(x)cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/4+pin