What is the general solution for cos(x)*tan(x)-cos(x)=0 ?

The general solution for cos(x)*tan(x)-cos(x)=0 is x= pi/4+pin

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

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

x = \frac{π}{4} + πn

Solution steps

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 (θ) = 653

- 5 sin^{2} (x) - 4 cos (x) = - 4

tan^{2} (θ) = \frac{1}{3}, 0 \leq θ \leq 2 π

4 sin (2 x) = 23

3 cos (2 θ) - 5 cos (θ) - 1 = 0

What is the general solution for cos(x)*tan(x)-cos(x)=0 ?
The general solution for cos(x)*tan(x)-cos(x)=0 is x= pi/4+pin