Observe if sinx + cosx = (cotx + 1)*1/cscx.

Expert Answers
sciencesolve eNotes educator| Certified Educator

I suggest you to focus on the right side. Notice that you need to expand the functions cot x and tan x to into fractions such that:

`sin x + cos x = (cos x/sin x + 1)/(1/sin x)`

You need to bring to a common denominator the terms to the numerator such that:

`sin x + cos x = ((cos x + sin x)/sin x)/(1/sin x)`

Reducing by sin x yields:

`sin x + cos x = cos x + sin x`

This relation proves the identity.

You may also focus on the left side where I suggest you to form the cotangent function, hence you need to divide both sides, to preserve identity, by sin x such that:

`1 + cos x/sin x = (cot x + 1)/(sin x*csc x)`

You need to remember that csc x is the reverse of sine function such that:

`csc x = 1/sin x`

`` `1 + cot x= (cot x + 1)/(sin x*(1/sin x))`

Reducing by sin x yields:

`1 + cot x = (cot x + 1)/1 =gt 1 + cot x = 1 + cot x`

Hence, it is of no importance which process of solving you choose, as you will have the same answer either way:`sin x + cos x = (cot x + 1)/csc x.`