Simplify cos(t)+tan(t)sin(t)

Problem

cos(t)+tan(t)*sin(t)

Solution

1. Use the quotient identity to rewrite the tangent function in terms of sine and cosine.

tan(t)=sin(t)/cos(t)

2. Substitute this identity into the original expression.

cos(t)+sin(t)/cos(t)*sin(t)

3. Multiply the sine terms in the second part of the expression.

cos(t)+sin2(t)/cos(t)

4. Find a common denominator to combine the terms by multiplying the first term by cos(t)/cos(t)

cos2(t)/cos(t)+sin2(t)/cos(t)

5. Combine the fractions over the single denominator.

(cos2(t)+sin2(t))/cos(t)

6. Apply the Pythagorean identity where sin2(t)+cos2(t)=1

1/cos(t)

7. Use the reciprocal identity to simplify the final fraction.

sec(t)

Final Answer

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

Want more problems? Check here!