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

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

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

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

cos (x)

from both sides

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

Factor

cos (x) tan (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

tan (\frac{θ}{2} - \frac{π}{6}) = - 1

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

tan (θ) = \frac{2}{2} csc (θ)

2 sin (x) cos (x) = \frac{1}{2}

tan (θ) = 0.75

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