Simplify sin(x)tan(x)+cos(x)

Problem

sin(x)*tan(x)+cos(x)

Solution

1. Apply the identity for the tangent function, which is tan(x)=sin(x)/cos(x)

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

2. Multiply the terms in the first part of the expression.

sin2(x)/cos(x)+cos(x)

3. Find a common denominator to combine the terms by multiplying cos(x) by cos(x)/cos(x)

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

4. Combine the numerators over the single denominator.

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

5. Apply the Pythagorean identity sin2(x)+cos2(x)=1

1/cos(x)

6. Use the reciprocal identity where 1/cos(x)=sec(x)

sec(x)

Final Answer

sin(x)*tan(x)+cos(x)=sec(x)

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