Simplify (1+cot(x))/(csc(x))

Problem

(1+cot(x))/csc(x)

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the identities cot(x)=cos(x)/sin(x) and csc(x)=1/sin(x)

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

2. Find a common denominator for the terms in the numerator to combine them into a single fraction.

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

3. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

(sin(x)+cos(x))/sin(x)⋅sin(x)

4. Cancel the common factor of sin(x) from the numerator and the denominator.

sin(x)+cos(x)

Final Answer

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

Want more problems? Check here!