Question

D/dx(sin x/2+cos x) = (a + b cos x)/(2+cos x)^2 find a and b.​

Answer 1

Answer:

a = 1 and b = 2

Step-by-step explanation:

Using the Quotient Rule>

d/dx[(sin x)/(2+cos x) ]

=   [(2 + cos x) * cosx -  sin x * - sin x)]  /  (2 + cos x)^2

= 2cos x + cos^2x + sin ^2 x) /  (2 + cos x)^2

But cos^2x + sin^2x = 1 so we have:

(1 +  2 cos x)  /   (2 + cos x)^2

- so a = 1 and b = 2.