Verified answer

dy/dx= -(π/2)(cosec(πx/12))^2

At x= 3, dy/dx

= -(π/2)(cosec((π/4))^2

= -(π/2)(2)

= -π

The equation of the tangent is of the form y= mx+c, where m is the gradient and c is the y-intercept.

At x= 3, y

= 6cot(π/4)

= 6

6= (-3π)+c

c= 6+3π

Thus, the equation of the tangent to the curve at x= 3 is y= -πx+3π+6. I hope this helps and feel free to send me an e-mail if you have any doubts!

tangent equation

y - f(3) = f '(3) (x-3)