Question

If sin theta +cos theta=root3 then prove that tan theta+ cot theta =1

Answer 1

Step-by-step explanation:

sinA+cosA=√3

(sinA+cosA)²=(√3)²

sin²A+cos²A+2sinAcosA=3

1+2sinAcosA=3

2sinAcosA=2

sinAcosA=1..........(1)

tanA+cotA

=(sinA/cosA)+(cosA/sinA)

=(sin²A+cos²A)/sinAcosA

=1/1

=1