Question

cot^4a - cot^2a=1 then cot^2a=?

Answer 1

${\bold{\huge{\underline{\blue{\sf{Given:}}}}}}$

${\bold{\sf{cot⁴a-cot²a=1}}}$

${\bold{\huge{\underline{\pink{\sf{To \: Find:}}}}}}$

${\bold{\sf{Value\:of\:cot²a}}}$

${\bold{\huge{\underline{\red{\sf{Formula:}}}}}}$

${\boxed{\sf{x= \frac{-b± \sqrt{b²-4ac}}{2a}}}}$

${\bold{\sf{Here, \: ax²+bx+c=0}}}$

${\bold{\huge{\underline{\green{\sf{Solution:}}}}}}$

${\boxed{\sf{Let\:\:\:cot²a=x}}}$

${\bold{\sf{cot⁴a-cot²a=1}}}$

${\bold{\sf{x²-x=1}}}$

${\bold{\sf{x²-x-1=0}}}$

${\bold{\sf{x= \frac{-(-1)± \sqrt{(-1)²-4(1)(-1)}}{2(1)}}}}$

${\bold{\sf{x= \frac{1±\sqrt{5}}{2}}}}$

Case-(i)

${\bold{\sf{x= \frac{1+ \sqrt{5}}{2}}}}$

${\boxed{\sf{cos²a= \frac{1y+ \sqrt{5}}{2}}}}$

Case-(ii)

${\bold{\sf{x= \frac{1- \sqrt{5}}{2}}}}$

${\boxed{\sf{cos²a= \frac{1- \sqrt{5}}{2}}}}$

Answer 2

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