If with prove that

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Solution

Given,

cosy=xcos( a+y )(1)

Differentiate both sides with respect to x.

d dx { cosy }= d dx { xcos( a+y ) } −siny dy dx =cos( a+y ) d dx ( x )+x× d dx { cos( a+y ) } −siny dy dx =cos( a+y )+x{ −sin( a+y ) } dy dx [ xsin( a+y )−siny ] dy dx =cos( a+y )

From equation (1), we get,

cosy=xcos( a+y ) x= cosy cos( a+y )

Substitute the value of x in the above equation.

[ cosy cos( a+y ) ×sin( a+y )−siny ] dy dx =cos( a+y ) [ cosy×sin( a+y )−siny×cos( a+y ) ] dy dx = cos 2 ( a+y ) sin( a+y−y ) dy dx = cos 2 ( a+y ) dy dx = cos 2 ( a+y ) sina

Hence, it is proved that dy dx = cos 2 ( a+y ) sina .

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Similar questions

If with prove that

If, prove that

\cos y = x \cos (a + y), with \cos a \neq \pm 1, prove that \frac{d y}{d x} = \frac{\cos^{2} (a + y)}{\sin a}

\cos y = x \cos (a + y), with \cos a \neq \pm 1, prove that \frac{d y}{d x} = \frac{\cos^{2} (a + y)}{\sin a}

cos y = x cos (a + y)

cos a \neq \pm 1

\frac{d y}{d x} = \frac{{cos}^{2} (a + y)}{sin a}

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