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Question

If y=x4x2+1x2+3x+1 and dydx=ax+b then the value of a+b is equal to

A
cot5π8
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B
cot5π12
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C
tan5π12
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D
tan5π8
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Solution

The correct option is B cot5π12
dydx=(4x32x)(x2+3x+1)(2x+3)(x4x2+1)(x2+3x+1)2
=4x5+43x4+4x32x323x22x2x5+2x32x3x4+3x23(x2+3x+1)2
=2x5+33x4+4x33x24x3(x2+3x+1)2
which is equal to (2x3)
so, a=2 and b=3
a+b=23
cot75=cot(45+30)=cot45cot301cot45+cot30
=311+3=(31)(13)(1+3)(13)
=(3+123)13=23
Hence, option B is correct

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