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

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

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

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

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

Solution steps

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

Subtract

cos^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

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

sin (x) - cos (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

x, sin (x - y) = 0

cos (2 θ) = 0.4

6 sin (x) + 2 cos (x) = 0

cos (2 x) = - \frac{3}{2}, 0 \leq x \leq 2 π

tan (θ) = \frac{5}{2}

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