What is the general solution for solvefor x,sec(x)tan(x)=2sqrt(3) ?

The general solution for solvefor x,sec(x)tan(x)=2sqrt(3) is x= pi/3+2pin,x=(2pi)/3+2pin

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solvefor x,sec(x)tan(x)=2sqrt(3)

solve for

x, sec (x) tan (x) = 23

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

Solution steps

sec (x) tan (x) = 23

Subtract

23

from both sides

sec (x) tan (x) - 23 = 0

Express with sin, cos

\frac{sin ( x ) - 2 cos ^{2} ( x ) 3}{cos ^{2} ( x )} = 0

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

sin (x) - 2 cos^{2} (x) 3 = 0

Rewrite using trig identities

sin (x) - (1 - sin^{2} (x)) \cdot 23 = 0

Solve by substitution

sin (x) = \frac{3}{2}, sin (x) = - \frac{2 3}{3}

sin (x) = \frac{3}{2} : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

sin (x) = - \frac{2 3}{3} :

No Solution

Combine all the solutions

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

4 sin (θ) - 4 cos (θ) = 2

4 sin (x) + 22 = 0

sin (4 x) + sin (2 x) = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

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

2 cos (2 x) = 2

What is the general solution for solvefor x,sec(x)tan(x)=2sqrt(3) ?
The general solution for solvefor x,sec(x)tan(x)=2sqrt(3) is x= pi/3+2pin,x=(2pi)/3+2pin