Question

Prove:
sqrt(cosec^A-1) = cosAcosecA

Answer 1

\[\sqrt{cosec^2A-1}=cosAcosecA\]

Answer 2

use, cosec^2 = 1+cot^2

Answer 3

\[\sqrt{(1+\cot^2A)-1}\]

Answer 4

\[\sqrt{\cot^2A}\]

Answer 5

??

Answer 6

yes.
=cot = cos/sin
and 1/sin =cosec

Answer 7

use \[\frac{ 1 }{ \sin ^{2}A } = \csc ^{2}A\] to replace the cosec^2A

Answer 8

After, you can find the LCM which is sin^2 A.

Answer 9

Realize you get a numerator which is 1-sin^2 A which can be replaced by cos^2 A using the identity: \[\cos ^{2}A + \sin ^{2}A = 1\]