If siny=x sin(a+y) prove that dy/dx=sin^2(a+y)/sina
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Answer:
Step-by-step explanation:
Siny = x Sin(a + y)
x = Siny/Sin(a + y)
Differentiating w.r.t. y, using the Quotient Rule, we have,
dx/dy = Sin(a + y) d/dy{Siny} - Siny. d/dy{Sin(a + y)} / Sin² (a + y)
= Sin(a + y) * Cosy - Siny * Cos(a + y) *d/dy(a + y), ...., / Sin² (a+y) [Chain rule]
= Sin(a + y) *Cosy - Siny * Cos (a + y) / Sin²(a + y)
= Sin (a + y - y)/Sin² (a + y)
= Sin a / Sin² (a + y)
dy/dx = 1 / (dx/dy) = 1 / [Sin a / Sin² (a + y)]
= Sin² (a + y) / Sin a
=R.H.S
Hence proved.
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