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=(3pi)/4+pin

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cos(x)tan(x)+cos(x)=0

cos (x) tan (x) + cos (x) = 0

x = \frac{3 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{3 π}{4} + πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{3 π}{4} + πn

Since the equation is undefined for:

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

x = \frac{3 π}{4} + πn

2 sin^{2} (2 θ) = 1 + sin (2 θ)

sin (2 x) - cos (x) = 0, 0 \leq x \leq 2 π

csc (θ) = - \frac{2}{3}

2 cos (\frac{x}{2}) + 3 = 0

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

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=(3pi)/4+pin