Question

SinA+cosA=root2 then evaulate tanA+cotA

Answer 1

Answer

 $Sin A + Cos A = \sqrt{2}$ .....................(1)

=  $Sin^2 A + Cos ^2A + 2SinA *Cos A = 2$  {Squaring Both sides }

=  $1+ 2SinA * Cos A = 2$

=  $SinA + CosA = 1/2$ ...........................(2)

From L.H.S

$Tan A + CotA$

=  $SinA/CosA= CosA/ SinA$

=  $Sin^2A +Cos^2A/ CosA*SinA = 1/1/2$

Hence,

Tan A+Cot A =  2