# What is the equation of the tangent line of #f(x)=4secx–8cosx# at #x=(pi/3)#?

Determine where the tangent line will cross.

The two following trigonometric identities must be understood in order to find the derivative of the function, which is necessary in order to determine the slope of the tangent line:

Derivatively speaking,

Providing the tangent line's equation

The original function and the zoomed-in tangent line are graphed:

graph{y-4-12sqrt3(x-pi/3))=0 [-1.5, 2, -6, 15]} as (4secx-8cosx-y)

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The equation of the tangent line of f(x)=4secx–8cosx at x=(pi/3) is y = -2√3x + 4√3 - 4.

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