Question

Solve this quick plz 7th question

Answer 1

Given, root of 1+cos theta/1-cos theta can be written as

             = root (1+cos theta)(1+cos theta)/(1-cos theta)(1+cos theta)

            = root (1+cos theta)^2/sin^2 theta

           = 1+cos theta/sin theta

           = 1/sin theta + cos theta/sin theta
 
           = cosec theta + cot theta.


Hope this helps!

Answer 2

LHS=√1+cosA/1-cosA
rationalisation
=√(1+cosA)^2/1-cos^2A
=√(1+cosA)^2/sin^2A
=√(1+cosA/sinA)^2
=(1+cosA/sinA)
=1/sinA+cosA/sinA
=cosecA+cotA proved