What is the general solution for 4sin(x)=sqrt(3)sec(x) ?

The general solution for 4sin(x)=sqrt(3)sec(x) is x= pi/6+pin,x= pi/3+pin

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4sin(x)=sqrt(3)sec(x)

4 sin (x) = 3 sec (x)

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

Solution steps

4 sin (x) = 3 sec (x)

Subtract

3 sec (x)

from both sides

4 sin (x) - 3 sec (x) = 0

Express with sin, cos

\frac{- 3 + 4 cos ( x ) sin ( x )}{cos ( x )} = 0

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

- 3 + 4 cos (x) sin (x) = 0

Rewrite using trig identities

- 3 + 4 \cdot \frac{sin ( 2 x )}{2} = 0

4 \cdot \frac{sin ( 2 x )}{2} = 2 sin (2 x)

- 3 + 2 sin (2 x) = 0

Move

3

to the right side

2 sin (2 x) = 3

Divide both sides by

2

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

General solutions for

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

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

Solve

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

Solve

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

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

csc (θ) = 0.77

x, - cos (y) = sin (x)

3 cos^{2} (θ) - 10 = 0

\frac{sin ( x ) + cos ( x )}{sin ( x )} = 1 \frac{1}{tan ( x )}

What is the general solution for 4sin(x)=sqrt(3)sec(x) ?
The general solution for 4sin(x)=sqrt(3)sec(x) is x= pi/6+pin,x= pi/3+pin