​If sin theta + cos theta = root 3. then prove that tan theta + cot theta = 1

Sina + cosa = √3 . Squaring both sides we get : sin²a + cos²a + 2sina cosa = 3. Therefore 1 + 2 sina cosa = 3 :- 2 sina cosa = 2 :- sina cosa = 1 Through this we can solve as in the pic

( Sin theta + cos theta)^2= 3 
Sin^2theta + cos^2 theta + 2*sin theta*cos theta=3 

1+2*sin theta*cos theta=3 

Therefore, 
Sin theta*cos theta=1 



Tan theta+ cot theta = 1 

Sin theta/cos theta + cos theta/ sin theta = 1 

Sin^2 theta + cos^2 theta/sin theta*cos theta=1 

1/ sin theta* cos theta = 1 

Therefore, 

Sin theta* cos theta = 1 = sin theta + cos theta