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

The general solution for tan(x)cos(x)=cos(x) is x= pi/4+pin

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tan(x)cos(x)=cos(x)

tan (x) cos (x) = cos (x)

x = \frac{π}{4} + πn

Solution steps

tan (x) cos (x) = cos (x)

Subtract

cos (x)

from both sides

tan (x) cos (x) - cos (x) = 0

Factor

tan (x) cos (x) - cos (x) : cos (x) (tan (x) - 1)

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

Solving each part separately

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

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

tan (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

Since the equation is undefined for:

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

x = \frac{π}{4} + πn

4 cos^{2} (θ) - 2 = - 1

sinh (x) = \frac{7}{24}, cosh (x)

2 sin (x) + sin (2 x) = cos (x) + 1

sin (a) = \frac{15}{17}

cot (t) = 0

What is the general solution for tan(x)cos(x)=cos(x) ?
The general solution for tan(x)cos(x)=cos(x) is x= pi/4+pin