Question

Find dy/dx at x=45° if y=2-3cosx /sinx​

Answer 1

Answer:

6 - 2√2

Step-by-step explanation:

Given Find dy/dx at x=45° if y=2-3cosx /sinx​

Consider y = (2 - 3 cos x) / sin x

                y = 2 /sin x - 3 cos x / sin x

              y = 2 cosec x - 3 cot x

Now differentiating we get

            dy/dx = d/dx (2 cosec x - 3 cot x)

                      = 2 d/dx( cosec x - 3 d/dx(cot x)

We know that d/dx (cosec x) = - cosecx cot x

                         d/dx (cotx) = - cosec^2 x

  So dy/dx = 2(- cosecx cotx - 3 (- cosec^2 x)

                 = - 2 cosecx cot x + 3 cosec^2 x

  Now we need to put values that is x = π / 4 or 45 degree

           dy / dx = - 2 cosec 45 cot 45 + 3 cosec^2 45

                     = -2 √2 x 1 + 3 x (√2)^2

                      = - 2√2 + 2 x 3

       So dy/dx = 6 - 2√2