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[" 18.If "y=sin x*cos2x," prove that "],...

[" 18.If "y=sin x*cos2x," prove that "],[qquad (dy)/(dx)=y(cot x-2tan2x)]

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If y=sin x*cos(2x) then prove that (dy)/(dx)=y[cot x-2tan2x]

If y=sin x*cos(2x) then prove that (dy)/(dx)=y[cot x-2tan2x]

If y=sinx.cos(2x) then prove that (dy)/(dx)=y[cotx-2tan2x]

(dy)/(dx) + y cot x = sin 2x

if y=tan^(-1)((sin x)/(1+cos x)) prove that (dy)/(dx)=(1)/(2)

If (sin x)^(y)=(cos y)^(x), prove that (dy)/(dx)=(log cos y-y cot x)/(log sin x+x tan y)

If (sin x)^(y)=(cos y)^(x), prove that (dy)/(dx)=(log cos y-y cot x)/(log sin x+x tan y)

If y = ( tan x)/( 1+ tan^2 x), Prove that (dy)/(dx) = cos 2x.

If y=e^(x)(sin x+cos x), prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)=2y=0

If siny=x sin(a+y) , prove that, (dy)/(dx)=(sin a)/(1-2x cos a +x^(2)) .