Simplify sin(B)tan(B)+cos(B)

Problem

sin(B)*tan(B)+cos(B)

Solution

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

sin(B)sin(B)/cos(B)+cos(B)

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

sin2(B)/cos(B)+cos(B)

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

sin2(B)/cos(B)+cos2(B)/cos(B)

4. Combine the fractions over the single denominator cos(B)

(sin2(B)+cos2(B))/cos(B)

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

1/cos(B)

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

sec(B)

Final Answer

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

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