Simplify sec(pi/4)+9csc(pi/6)

Problem

sec(π/4)+9*csc(π/6)

Solution

1. Evaluate the secant term by using the reciprocal identity sec(θ)=1/cos(θ) Since cos(π/4)=√(,2)/2 then sec(π/4)=2/√(,2)=√(,2)

2. Evaluate the cosecant term by using the reciprocal identity csc(θ)=1/sin(θ) Since sin(π/6)=1/2 then csc(π/6)=2

3. Substitute the values back into the original expression.

√(,2)+9*(2)

4. Multiply and combine the terms to reach the final simplified form.

√(,2)+18

Final Answer

sec(π/4)+9*csc(π/6)=√(,2)+18

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