Question

If sin theta + cos theta =√3
Prove tan theta + cot theta =1​

Answer 1

sin(t) + cos(t) = √3 => sin^2(t) + cos^2(t) + 2sin(t)cos(t) = 3 => sin(t)cos(t) = 1

tan(t) + cot(t) = (1 + tan^2(t))/tan(t) = sec^2(t)/tan(t) = 1/cos^2(t) * cos(t)/sin(t) = 1/(cos(t)*sin(t))

= 1/1 = 1....

Proved