Question

Please solve this question which u know very well

Answer 1

Given sin theta + cos theta = root 2.

         Squaring on both sides, we get

         (sin theta + cos theta)^2 = (root 2)^2

 We know that (a+b)^2 = a^2+b^2+2ab.

         (sin^2 theta + cos^2 theta + 2 sin theta cos theta) = 2

We know that sin^2 theta + cos^2 theta = 1

         1 + 2 sin theta cos theta = 2

           2 sin theta cos theta = 1

           sin theta cos theta = 1/2     ---- (1)


Given tan theta + cot theta

         = sin theta/cos theta + cos theta/sin theta

        = sin^2 theta + cos^2 theta/sin theta cos theta

        = 1/1/2 (From (1) - sin theta cos theta = 1/2)

        = 2.


Therefore tan theta + cot theta = 2.


Hope this helps!