What is the general solution for (sqrt(3)tan(x))/(sec(x))-cos(x)=0 ?

The general solution for (sqrt(3)tan(x))/(sec(x))-cos(x)=0 is x= pi/6+pin

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(sqrt(3)tan(x))/(sec(x))-cos(x)=0

\frac{3 tan ( x )}{sec ( x )} - cos (x) = 0

x = \frac{π}{6} + πn

Solution steps

\frac{3 tan ( x )}{sec ( x )} - cos (x) = 0

Simplify

\frac{3 tan ( x )}{sec ( x )} - cos (x) : \frac{3 tan ( x ) - cos ( x ) sec ( x )}{sec ( x )}

\frac{3 tan ( x ) - cos ( x ) sec ( x )}{sec ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

- 1 + 3 tan (x) = 0

Move

1

to the right side

3 tan (x) = 1

Divide both sides by

3

tan (x) = \frac{3}{3}

General solutions for

tan (x) = \frac{3}{3}

x = \frac{π}{6} + πn

2 cos (2 x) = 2

sec^{2} (θ) - 2 tan (θ) = 0

sin (2 x) - cos (2 x) = 2

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

3 tan (2 x) - 3 = 0

What is the general solution for (sqrt(3)tan(x))/(sec(x))-cos(x)=0 ?
The general solution for (sqrt(3)tan(x))/(sec(x))-cos(x)=0 is x= pi/6+pin