Question

Simplify csc θ + cot θ

Answer 1

csc θ + cot θ

From trigonometric identities

`\csc(θ) = (1)/( \sin(θ) )`

And

`\cot(θ) = ( \cos(θ) )/( \sin(θ) )`

So we have

`(1)/( \sin(θ) ) + ( \cos(θ) )/( \sin(θ) )`

Find the LCM

The LCM is sin θ

So we have

`(1)/( \sin(θ) ) + ( \cos(θ) )/( \sin(θ) ) = (1 + \cos(θ) )/( \sin(θ) )`

And

`(1 + \cos(θ) )/( \sin(θ) ) = \cot( (θ)/(2) )`

So we have the final answer as

`\cot( (θ)/(2) )`

Hope this helps you