Question

SinA+cosA=root3.then prove that tanA+cotA=1

Answer 1

sinA+cosA=√3
Squaring both sides,
(sinA+cosA)²=3
or, sin²A+2sinAcosA+cos²A=3
or, 1+2sinAcosA=3
or, 2sinAcosA=3-1
or, 2sinAcosA=2
or, sinAcosA=1 -----------(1)
∴, tanA+cotA
=sinA/cosA+cosA/sinA
=(sin²A+cos²A)/sinAcosA
=1/sinAcosA
=1/1 [using (1)]
=1 (Proved)

Answer 2

sinA+cosA = √3

squaring both sides

(sinA + cosA)² = 3

1+2sinAcosA = 3

2sinAcosA = 2

sinAcosA = 1

Now

tanA + cotA

=sinA/cosA + cosA/sinA

=sin²A+cos²A/sinAcosA

=1/sinAcosA

=1/1

=1