If cos y-x cos a-y- cosa-1 prove that d y-d x-cos 2a-y-sin a

Cos y=x cos(a+y) ⇒ x =cos y/cos(a+y) dx/dy=d/dy [cos y/cos(a+y) ]=cos(a+y)sin y+cos ysin(a+y)/cos^2(a+y) dx/dy=sin(a+y y)/cos^2(a+y) dx/dy=sin a/cos^2(a+y)⇒dx/ ...

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Standard XII

Mathematics

Parametric Differentiation

If cos y=x co...

Question

If $c o s y = x c o s (a + y), c o s a \neq 1$ prove that $\frac{d y}{d x} = \frac{c o s^{2} (a + y)}{s i n a}$

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Solution

$c o s y = x c o s (a + y) \Rightarrow x = \frac{c o s y}{c o s (a + y)} \frac{d x}{d y} = \frac{d}{d y} [\frac{c o s y}{c o s (a + y)}] = \frac{c o s (a + y) s i n y + c o s y s i n (a + y)}{c o s^{2} (a + y)} \frac{d x}{d y} = \frac{s i n (a + y - y)}{c o s^{2} (a + y)} \frac{d x}{d y} = \frac{s i n a}{c o s^{2} (a + y)} \Rightarrow \frac{d x}{d y} = \frac{c o s^{2} (a + y)}{s i n a}$

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If cos y=x cos (a+y),cos a≠1 prove that dydx=cos2(a+y)sin a

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If $c o s y = x c o s (a + y), c o s a \neq 1$ prove that $\frac{d y}{d x} = \frac{c o s^{2} (a + y)}{s i n a}$