What is the general solution for sec(x)=2csc(x) ?

The general solution for sec(x)=2csc(x) is x=1.10714…+pin

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sec(x)=2csc(x)

sec (x) = 2 csc (x)

x = 1.10714 \dots + πn

Solution steps

sec (x) = 2 csc (x)

Subtract

2 csc (x)

from both sides

sec (x) - 2 csc (x) = 0

Express with sin, cos

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

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

sin (x) - 2 cos (x) = 0

Rewrite using trig identities

tan (x) - 2 = 0

Move

2

to the right side

tan (x) = 2

Apply trig inverse properties

x = arctan (2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn

cos^{2} (x) = 0.75

tan (x) = \frac{π}{2}

tan (x) = \frac{π}{4}

13 cos (x) + 7 = - cos (x)

cos^{2} (x) = 0.25

What is the general solution for sec(x)=2csc(x) ?
The general solution for sec(x)=2csc(x) is x=1.10714…+pin