Question

√1-cos theta÷√1+cos theta=cosec theta-cot theta​

Answer 1

Acc. to me,

Here I suppose theta =y

Your question,

           LHS                           RHS

√1-cos y÷√1+cos y   =    cosec y-cot y

First rationalise LHS by √1-cos y

√1-cos y             √1-cos y

_______     *     ________

√1+cos y             √1-cos y

Now you see = 1-cos y

                         ______

                         (√1+cos y)(√1-cos y)

Here you use (a+b)(a-b)=a²-b²     then

1 -cos y

______

(√1²-cos²y)------------use 1-cos²y=sin²y

so

1 - cos y

______

sin y    

Seperate both

1/sin y - cos y/sin y

1/sin y =cosec y and cos y/sin y= cot y

=cosec y - cot y -----------Proved

I hope you understand