Question

1 + cos theta divided by 1 - cos theta is equal to cosec theta + cot theta whole square ​

Answer 1

Answer:

I think that it's wrong.

Answer 2

1 + cos∅/1-cos∅ = (cosec ∅ + cot ∅)²

1 + cos∅ x 1 + cos∅/1-cos∅ x 1 + cos∅ (dividing by the conjugate of denominator)

(1 + cos∅)²/1-cos²∅        (sin²∅ + cos²∅ = 1) so (1-cos²∅ = sin²∅)

(1 + cos∅)²/sin²∅            

1 + 2cos∅ + cos²∅/sin²∅

1/sin²∅ + 2cos∅/sin²∅ + cos²∅/sin²∅

cosec²∅ + tan²∅ + 2cos∅/sin²∅ = L.H.S

let us take the R.H.S

(cosec ∅ + cot ∅)²

cosec²∅ + tan²∅ + 2cosec∅xcot ∅

cosec²∅ + tan²∅ + 2/sin∅ x cos∅/sin∅  (expanding cosec and cot)

cosec²∅ + tan²∅ + 2cos∅/sin²∅ = L.H.S

therefore,L.H.S = R.H.S , 1 + cos∅/1-cos∅ = (cosec ∅ + cot ∅)²

                                    HENCE PROVED

                                  HOPE THIS HELPS!!!