let A denotes the value of expression
X4 + 4X3 + 2X2 - 4X + 7 when X= cot11pi/8
and B denotes the value of expression
( 1- cos8y)/ tan24y + (1+cos8y)/ cot24y when y=9°
the value of (A-B) is ____
the question is integer type (0-9)
i know B is easy bt wht abt A?
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1 Answers
1708\textbf{For Calculation of A}::\\\\ \mathbf{x=Cot\left(\frac{11\pi}{8}\right)=Cot\left(2\pi-\frac{5\pi}{8}\right)=-cot\left(\frac{5\pi}{8}\right)=-cot\left(\frac{\pi}{2}+\frac{\pi}{8}\right)=tan\left(\frac{\pi}{8}\right)=\sqrt{2}-1}$\\\\ Now Here $\mathbf{x=\sqrt{2}-1\Leftrightarrow (x+1)^2=2\Leftrightarrow (x^2+2x+1)=2\Leftrightarrow\boxed{ x^2+2x=1}}$\\\\ OR $\mathbf{(x^2+2x)^2=1\Leftrightarrow x^4+4x^2+4x^3=1\Leftrightarrow \boxed{x^4+4x^3+2x^2=1-2x^2}}$\\\\ \textbf{Now Put That value in} $\mathbf{x^4+4x^3+2x^2-4x+7=1-2x^2-4x+7=8-2(x^2+2x)=8-2.(1)=6}$
