# How do you find an equation of the tangent line to the curve at the given point #y=secx - 2cosx# and #(pi/3, 1)#?

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To find the equation of the tangent line to the curve y = sec(x) - 2cos(x) at the point (π/3, 1), we need to find the derivative of the function and evaluate it at the given point.

The derivative of y = sec(x) - 2cos(x) can be found using the chain rule and product rule. The derivative is dy/dx = sec(x)tan(x) + 2sin(x).

To find the slope of the tangent line at (π/3, 1), substitute π/3 into the derivative: dy/dx = sec(π/3)tan(π/3) + 2sin(π/3).

Evaluate the trigonometric functions: sec(π/3) = 2, tan(π/3) = √3, and sin(π/3) = √3/2.

Substitute the values: dy/dx = 2√3 + 2(√3/2) = 2√3 + √3 = 3√3.

The slope of the tangent line at (π/3, 1) is 3√3.

Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, substitute the values: y - 1 = 3√3(x - π/3).

Simplify the equation: y = 3√3x - 3π + π√3 + 1.

Therefore, the equation of the tangent line to the curve y = sec(x) - 2cos(x) at the point (π/3, 1) is y = 3√3x - 3π + π√3 + 1.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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