Question

How do you simplify 1/(tanx+cotx)?

Answer 1

`cosxsinx`

Explanation:

`1/(tanx+cotx)`

Quotient identities:

`1/(sinx/cosx+cosx/sinx)=`

`1/(sin^2x/(cosxsinx)+cos^2x/(cosxsinx))=`

`1/((sin^2x+cos^2x)/(cosxsinx))=`

`(cosxsinx)/(sin^2x+cos^2x)=`

Pythagorean Identity:
`cosxsinx`

The best I could possibly do in terms of simplification

Answer 2

(sin 2x)/2

Explanation:

`1/(tan x+ cot x) = 1/((sin x/(cos x)) + cos x/(sin x)) =`
`= (sin x.cos x)/(sin^2 x + cos^2 x) = sin x.cos x = (sin 2x)/2`
Reminder:
2sin x.cos x = sin 2x
`sin^2 x + cos^2 x = 1`