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Question
If `y = (sin(x + 9))/cosx` then `(dy)/(dx)` at x = 0 is ______.
Options
cos 9
sin 9
0
1
Solution
If `y = (sin(x + 9))/cosx` then `(dy)/(dx)` at x = 0 is cos 9.
Explanation:
Given `y = (sin(x + 9))/cosx`
`(dy)/(dx) = (cosx * cos(x + 9) - sin(x + 9)(- sin x))/(cos^2x)`
= `(cos x cos(x + 9) + sin x sin(x + 9))/(cos^x)`
= `(cos(x + 9 - x))/(cos^2x)`
= `cos9/(cos^2x)`
∴ `((dy)/(dx))_("at" x = 0) = cos9/(cos^2 0)`
= `cos9/(1)^2`
= cos 9
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