Question

Find an equation of the tangent line to the curve at the given point.
y = csc (x) - 2 sin (x) P=(pi/6,1)

Answer 1

first finding the derivative of equation
y'=-csc(x)cot(x) - 2cos(x) <---also the slope equation for tangent lines at every point on the graph

Given the point (pi/6,1)
Finding slope m=y'(pi/6)= -csc(pi/6)cot(pi/6) - 2cos(pi/6) = -3squrtroot(3)
Equation for tangent line
y-y1=m(x-x1)
y-1=-3squrtroot(3)(x-pi/6)
y= [-3\sqrt{3} + \pi \sqrt{3}/2 +1\]

Answer 2

\[y= -3\sqrt{3}x + \pi \sqrt{3}/2 +1\]