Question #88b3e

1 Answer
Feb 13, 2018

1/cosx

Explanation:

Convert everything to sinx and cosx:

(sinx/cosx+cosx/sinx)/(1/sinx)

Dividing by 1/sinx is the same as multiplying by the reciprocal sinx

(sinx)(sinx/cosx+cosx/sinx)

Distribute

sin^2x/cosx+(sinxcosx)/sinx

Simplify

sin^2x/cosx+cosx/1

The common denominator is cosx

sin^2x/cosx+cos^2x/cosx

Add fractions

(sin^2x+cos^2x)/cosx

sin^2x+cos^2x=1 (Pythagorean Identity) Sooooo:

(sin^2x+cos^2x)/cosx=1/cosx

That's your answer in terms of cosx. Most people would convert 1/cosx to secx, though.