Question

Simplify csc θ + cot θ

Answer 1

Answer:

csc θ + cot θ

From trigonometric identities

$\csc(θ) = \frac{1}{ \sin(θ) }$

And

$\cot(θ) = \frac{ \cos(θ) }{ \sin(θ) }$

So we have

$\frac{1}{ \sin(θ) } + \frac{ \cos(θ) }{ \sin(θ) }$

Find the LCM

The LCM is sin θ

So we have

$\frac{1}{ \sin(θ) } + \frac{ \cos(θ) }{ \sin(θ) } = \frac{1 + \cos(θ) }{ \sin(θ) }$

And

$\frac{1 + \cos(θ) }{ \sin(θ) } = \cot( \frac{θ}{2} )$

So we have the final answer as

$\cot( \frac{θ}{2} )$

Hope this helps you