Evaluate sec(pi/3)tan(pi/3)

Problem

sec(π/3)*tan(π/3)

Solution

1. Identify the values of the trigonometric functions at the angle π/3 radians, which is equivalent to 60

2. Evaluate the secant function using the reciprocal identity sec(θ)=1/cos(θ)

cos(π/3)=1/2

sec(π/3)=1/(1/2)=2

3. Evaluate the tangent function using the ratio tan(θ)=sin(θ)/cos(θ) or the known value for 60

sin(π/3)=√(,3)/2

tan(π/3)=(√(,3)/2)/(1/2)=√(,3)

4. Multiply the two results together to find the final value.

2⋅√(,3)=2√(,3)

Final Answer

sec(π/3)*tan(π/3)=2√(,3)

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