Question

if sinA +cosA = x ,then show that : tanA + cotA =2/x²-1

Answer 1

sinA+cosA=x
squaring on both sides and proceed as shown

Answer 2

$tanA + cotA = 2/ x^{2} -1$ 
First I'm doing LHS 
$sinA/cosA + cosA/ sinA$
$sin^{2}A + cos^{2}A/sinAcosA$
$1/sinAcosA (sin^{2}A+ cos^{2} A = 1 )$
Now the RHS:
$2/(sinA+cosA)^{2}- 1$
[tex]2/sin^{2} A+ cos^{2} A+ 2sinAcosA-1 [/tex]
$2/1+2sinAcosA - 1$
$1/sinAcosA$
Hence proved