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

Problem

csc(x)/(tan(x)+cot(x))

Solution

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

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

2. Find a common denominator for the terms in the denominator of the main fraction.

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

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

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

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

1/sin(x)⋅(sin(x)*cos(x))/1

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

cos(x)

Final Answer

csc(x)/(tan(x)+cot(x))=cos(x)

Want more problems? Check here!