What is the general solution for cos^2(x)-tan(x)cos^2(x)=0 ?

The general solution for cos^2(x)-tan(x)cos^2(x)=0 is x= pi/4+pin

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cos^2(x)-tan(x)cos^2(x)=0

cos^{2} (x) - tan (x) cos^{2} (x) = 0

x = \frac{π}{4} + πn

Solution steps

cos^{2} (x) - tan (x) cos^{2} (x) = 0

Factor

cos^{2} (x) - tan (x) cos^{2} (x) : - cos^{2} (x) (tan (x) - 1)

- cos^{2} (x) (tan (x) - 1) = 0

Solving each part separately

cos^{2} (x) = 0 or tan (x) - 1 = 0

cos^{2} (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

3 tan (x) - 1 = 0, 0 \leq x \leq 2 π

6 + 12 sin (θ) = 0

t, cos (2 t) = sin (t)

tan (x) = 1.8

tan (x) = 1.6

What is the general solution for cos^2(x)-tan(x)cos^2(x)=0 ?
The general solution for cos^2(x)-tan(x)cos^2(x)=0 is x= pi/4+pin