Question

prove :1÷1+cosA+1÷1-cosA=2cosec^2A

Answer 1

LHS:
=1/(1+cosA)+1/(1-cosA)
=(1-cosA+1+cosA)/(1+cosA)×(1-cosA)
=(2)/(1-cos²A)
[using sin²A+cos²A=1]
=2/(sin²A)
=2cosec²A [cosecA=1/sinA]
=RHS

Hence proved.

Answer 2

$To \ Prove : \frac{1}{1-cos^{2}(A) } + \frac{1}{1+cos^{2}(A) } = 2 cosec^{2} (A) \\ \\ = \frac{1+cos^{2}(A) +1-cos^{2}(A)}{1-cos^{2}(A) } \\ \\ = \frac{2}{sin^{2}(A) }\\ \\=\textgreater \ 2cosec ^{2} (A)$

Hence L.H.S = R.H.S
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Formulas used :-

★1- cos²(A) = sin²(A)
★1/sin(A) = cosec(A)