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Question

Find dydx, if y=tan−1(acosx−bsinxbcosx+asinx),abtanx>−1

A
2
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B
2
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C
1
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D
1
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Solution

The correct option is B 2
dydx , if y=tan1(acosxbsinxbCosx+asinx)

dydx=11+(acosxbsinxbcosx+asinx)2(bcosx+asinx)(asinxbcosx)(acosxbsinx)(bsinx+acosx)(bcosx+asinx)2

=(bcosx+asinx)2(bcosx+asinx)2+(acosxbsinx)2

=absinx.cosxb2cos2xa2sin2xabsinx.cosx(absinx.cosx+a2cos2x+b2sin2xabsinx)bx)(bcosx+ssinx)2

2absinx.cosxa2b2+2absinx.cosxa2b2b2cosx2+a2Sin2x+2absinx.cosx+a2Cos2x+b2sin2x2absinx.cosx

=2(a2+b2)(b2+a2)

=2

1071652_1071761_ans_43bf16e9bba9428f83e3bb2c3221a50c.png

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