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

Problem

sec(π/4)+4*csc(π/6)

Solution

1. Identify the values of the basic trigonometric functions at the given angles.

cos(π/4)=√(,2)/2

sin(π/6)=1/2

2. Apply the reciprocal identities for secant and cosecant.

sec(π/4)=1/cos(π/4)=2/√(,2)=√(,2)

csc(π/6)=1/sin(π/6)=1/(1/2)=2

3. Substitute these values back into the original expression.

√(,2)+4*(2)

4. Simplify the arithmetic expression.

√(,2)+8

Final Answer

sec(π/4)+4*csc(π/6)=8+√(,2)

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