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

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

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cot(x)cos(x)=cos(x)

cot (x) cos (x) = cos (x)

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

Solution steps

cot (x) cos (x) = cos (x)

Subtract

cos (x)

from both sides

cot (x) cos (x) - cos (x) = 0

Factor

cot (x) cos (x) - cos (x) : cos (x) (cot (x) - 1)

cos (x) (cot (x) - 1) = 0

Solving each part separately

cos (x) = 0 or cot (x) - 1 = 0

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

cot (x) - 1 = 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

tan^{4} (θ) - 20 tan^{2} (θ) + 64 = 0

sin (2 t) = - cos (2 t)

cos (3 θ) = sin (3 θ)

cos (5 x) = 1, 0 \leq x \leq \frac{π}{2}

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

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