Question

if sin theta+ cos theta= root 3 then prove that tan theta + cot theta = 1

Answer 1

sin theta + cos theta =√3
squaring both sides
(sin theta + cos theta)^2=(√3)^2
sin ^2 theta + cos ^2 theta +2sin theta cos theta=3
1+2sin theta cos theta = 3 (sin^2 theta + cos^2 theta = 1)
2 sin theta cos theta =2
sin theta cos theta = 1 eq.1.

tan theta + cot theta
sin theta/cos theta + cos theta/sin theta
sin^2 theta + cos^2 theta /sin theta cos theta
1/sin theta cos theta (sin^2 theta + cos^2 theta = 1)
1=1 (from eq. 1 )
=1