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

Question

Mathematics

Stephen Goodwin

7 March, 07:06

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

+3

Answers (1)

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Peyton Benitez · Answer 1

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.