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

The general solution for 2cos(x)=csc(x) is x= pi/4+pin

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2cos(x)=csc(x)

2 cos (x) = csc (x)

x = \frac{π}{4} + πn

Solution steps

2 cos (x) = csc (x)

Subtract

csc (x)

from both sides

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

Express with sin, cos

\frac{- 1 + 2 cos ( x ) sin ( x )}{sin ( x )} = 0

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

- 1 + 2 cos (x) sin (x) = 0

Rewrite using trig identities

- 1 + sin (2 x) = 0

Move

1

to the right side

sin (2 x) = 1

General solutions for

sin (2 x) = 1

2 x = \frac{π}{2} + 2 πn

Solve

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

cos (θ) = 0.3

sin^{5} (x) = 4 sin (x)

tan (x) = 2 + 3

sin (a) = \frac{11}{61}

4 sin (2 θ) = 2

What is the general solution for 2cos(x)=csc(x) ?
The general solution for 2cos(x)=csc(x) is x= pi/4+pin