What is the general solution for 3tan(x)= 1/(cos(x)) ?

The general solution for 3tan(x)= 1/(cos(x)) is x=0.33983…+2pin,x=pi-0.33983…+2pin

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3tan(x)= 1/(cos(x))

3 tan (x) = \frac{1}{cos ( x )}

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

Solution steps

3 tan (x) = \frac{1}{cos ( x )}

Subtract

\frac{1}{cos ( x )}

from both sides

3 tan (x) - \frac{1}{cos ( x )} = 0

Simplify

3 tan (x) - \frac{1}{cos ( x )} : \frac{3 tan ( x ) cos ( x ) - 1}{cos ( x )}

\frac{3 tan ( x ) cos ( x ) - 1}{cos ( x )} = 0

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

3 tan (x) cos (x) - 1 = 0

Rewrite using trig identities

- 1 + 3 sin (x) = 0

Move

1

to the right side

3 sin (x) = 1

Divide both sides by

3

sin (x) = \frac{1}{3}

Apply trig inverse properties

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

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

5 - tan^{2} (x) = 4

2 sec^{2} (θ) - 3 = tan^{2} (θ)

sin (π - x) + cos (x) = 0

sin (x) = - sin (2 x)

What is the general solution for 3tan(x)= 1/(cos(x)) ?
The general solution for 3tan(x)= 1/(cos(x)) is x=0.33983…+2pin,x=pi-0.33983…+2pin