Question

If sinA + cosA=√2 the find the value of tanA +cotA

Answer 1

sinA+cosA=root2
squaring both side
sin^2A+cos^2A+2sinAcosA=2
1+2sinAcosA=2
2sinAcosA=1
sinAcosA=1/2
tanA+cotA=sinA/ cosA + cosA/ sinA
take LCM
sin^2A+cos^2A/sinAcosA
=1/1/2
=2×1/1
=2
So,tanA+cotA=2

Answer 2

sinA + cosA = √3
(sinA + cosA)^2 = 3
or
(sinA)^2 + (casA)^2 + 2 sinA cosA = 3 
since (sinA)^2 + (casA)^2 =1 we get 2 sinA cos A = 2 or sinA cos A =1 
tan A + cotA = sinA/cosA + cosA/sinA = (sinA)^2 + (casA)^2 / sinA cos A = 1 / sinA cos A = 1