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

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

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sin(x)cos(x)=cos(x)

sin (x) cos (x) = cos (x)

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

Solution steps

sin (x) cos (x) = cos (x)

Subtract

cos (x)

from both sides

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

2 cos (2 θ) + 1 = 0, 0 \leq θ \leq 2 π

cot (x) sin (x) + cot (x) = 0

4 cos (2 θ) = 4 sin (2 θ)

tan (x) = - 3, 0 \leq x \leq 2 π

5 tan^{2} (A) - 7 = 8

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