Simplify 6tan(pi/4)+sin(pi/3)sec(pi/6)

Problem

6*tan(π/4)+sin(π/3)*sec(π/6)

Solution

1. Evaluate the tangent term using the unit circle value tan(π/4)=1

6*tan(π/4)=6*(1)=6

2. Evaluate the sine term using the unit circle value sin(π/3)=√(,3)/2

sin(π/3)=√(,3)/2

3. Evaluate the secant term by finding the reciprocal of cos(π/6)=√(,3)/2

sec(π/6)=1/cos(π/6)=2/√(,3)

4. Multiply the sine and secant values together.

sin(π/3)*sec(π/6)=√(,3)/2⋅2/√(,3)=1

5. Combine the results from the previous steps.

6+1=7

Final Answer

6*tan(π/4)+sin(π/3)*sec(π/6)=7

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