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+3 votes
58.1k views
in Differentiation by (30.0k points)
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If sin y = x cos(a + y), then \(\cfrac{dy}{d\mathrm x} \) is equal to

A. \(\cfrac{cos^2(a + y)}{cos\,a}\)

B. \(\cfrac{cos\,a}{cos^2\,(a+y)}\)

C. \(\cfrac{sin^2y}{cos\,a}\)

D. none of these

2 Answers

+5 votes
by (28.8k points)
selected by
 
Best answer

Correct option is A. \(\cfrac{cos^2(a + y)}{cos\,a}\)

sin y = x cos(a + y)

x = \(\cfrac{sin\,y}{cos(a+y)}\)

Differentiating w.r.t y we get,

+1 vote
by (15.0k points)

Correct option is A. \( \frac{\cos^2(a + y)}{\cos(a)}\)

\(x = \frac{\sin y}{\cos(a + y)}\)

\(\frac {dx}{dy} = \frac{\cos(a + y)\cos (y) - \sin(y) [-\sin (a + y)]}{[\cos (a + y)]^2}\)

\(\frac {dx}{dy} = \frac{\cos(a + y)\cos (y) +\sin(a + y) \sin(y) }{\cos^2 (a + y)}\)

\(\frac {dx}{dy}=\frac {\cos[(a + y)-y] }{\cos^2 (a + y)}\)

⇒ \(\frac{dy}{dx} = \frac{\cos^2(a + y)}{\cos(a)}\)

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