Given-that-cosecA-cotA-3-evaluate-cosecA-cotA-and-cosA-

Question Number 8310 by lepan last updated on 07/Oct/16

G i v e n t h a t c o s e c A + c o t A = 3 e v a l u a t e

c o s e c A - c o t A a n d c o s A .

Answered by prakash jain last updated on 08/Oct/16

1 + \cot^{2} A = {cosec}^{2} A

\Rightarrow {cosec}^{2} A - \cot^{2} A = 1

\Rightarrow (cosec A + \cot A) (cosec A - \cot A) = 1

G i v e n cosec A + \cot A = 3

\Rightarrow 3 (cosec A - \cot A) = 1

\Rightarrow (cosec A - \cot A) = \frac{1}{3}

- - - - - - - -

cosec A + \cot A = 3

(cosec A - \cot A) = \frac{1}{3}

2 cosec A = 3 + \frac{1}{3} \Rightarrow cosec A = \frac{5}{3}

\cot A = \frac{4}{3}

\sin A = \frac{3}{5}

\cos A = \pm \sqrt{1 - \sin^{2} A} = \pm \frac{4}{5}

since \cot A = \frac{4}{3} > 0

Only valid solution for \cos A = \frac{4}{5}