Question

Prove that cosec A + cot A = 1/ cosec A - cot A .

Answer 1

1/(csca - cota) =

1/(1/sina - cosa/sina) =

1/((1 - cosa)/sina) =

sina/(1 - cosa) =

(1 + cosa)/(1 + cosa) sina/(1 - cosa) =

(sina + sinacosa)/(1 - cos^2a) =

(sina + sinacosa)/sin^2a =

1/sina + cosa/sina =

csca + cota

Answer 2

Hence proved through rationalization that

cosec A + cot A = 1/ cosec A - cot A.

Step-by-step explanation:

⇒ R.H.S. = $\frac{1}{cosec A - CotA}$ ×$\frac{cosec A + Cot A}{Cosec A + Cot A}$       (through rationalization)

= $\frac{cosec A + CotA}{cosec^{2}A - Cot^{2}A}$

= Cosec A + Cot A    (L.H.S.)

Learn more: Trigonometry

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