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

Problem

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

Solution

1. Split the fraction into two separate terms by dividing each term in the numerator by the common denominator.

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

2. Cancel the common factors in each term. In the first term, sin(x) cancels out, and in the second term, cos(x) cancels out.

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

3. Apply the reciprocal trigonometric identities where sec(x)=1/cos(x) and csc(x)=1/sin(x)

sec(x)+csc(x)

Final Answer

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

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