Question

if tanA + 4/tanA = 5,find sinA and cosA

Answer 1

$TanA+ \frac{4}{TanA} =5$
$TanA = 5 - \frac{4}{TanA}$
$TanA = \frac{5TanA-4}{TanA}$
$Tan^{2} A=5TanA-4$
$tan^{2}A-5TanA+4=0$
$Tan^{2} A-4TanA-TanA+4=0$
$TanA(TanA-4)-1(TanA-4)=0$
(TanA-1)(TanA-4)=0
therefore TanA = 1
 And TanA = 4
When ,TanA = 1 then SinA = 1/√2   & CosA = 1/√2
And when TanA = 4 ,then SinA = 4/√17  & CosA = 1/√17