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) - 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

sin (θ) + cos (2 θ) = 0

3 sec (θ) - 4 = 0

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

cot (2 θ) = \frac{3}{4}

x, 0 = 4 - sec^{2} (x)

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