Question

if cosec theta + cot theta = p , then prove that cos theta = p^2 - 1 / p^2 + 1

Answer 1

given that cosec A + cot A = p _______(1)

ausing cosec ^ 2A - cot ^ 2A =( cos A + cotA) ( cosA - cot A)

1 = p ( cosec A - cot A)

1/ p = cosec
A - cotA ------(2)

1+ 2

p+ 1/p

p^ 2 + 1/p -------(3)

1- 2

1-2

p- 1/p

p^ 2 - 1/p ---------. (4)

(4) /(3)

p^ 2 - 1/p / P^ 2 +1 /p

here p gets cancelled

p^ 2 - 1/ p^ 2 +1

Hence proved

Answer 2

I made it.
Just by using p2-1/P2+1 as lhs