Simplify (cos(x))/(sin(x))+(sin(x))/(cos(x))

Problem

cos(x)/sin(x)+sin(x)/cos(x)

Solution

1. Find a common denominator by multiplying the first fraction by cos(x)/cos(x) and the second fraction by sin(x)/sin(x)

(cos(x)⋅cos(x))/(sin(x)⋅cos(x))+(sin(x)⋅sin(x))/(cos(x)⋅sin(x))

2. Combine the fractions over the common denominator sin(x)*cos(x)

(cos2(x)+sin2(x))/(sin(x)*cos(x))

3. Apply the Pythagorean identity sin2(x)+cos2(x)=1 to simplify the numerator.

1/(sin(x)*cos(x))

4. Rewrite using reciprocal identities where 1/sin(x)=csc(x) and 1/cos(x)=sec(x)

csc(x)*sec(x)

Final Answer

cos(x)/sin(x)+sin(x)/cos(x)=csc(x)*sec(x)

Want more problems? Check here!