Question

cosec A+cot A = sin A / 1-cos A​

Answer 1

Answer:

as cosec a=1/sin a

and cot a=cos a / sin a

so , L.H.S. = cosec a - cot a = 1 /sin a - cos a/ sin a

= (1-cos a) / sin a =(1- cos a)(1 + cos a) / sin a * (1 + cos a )

=1 - cos^2 (a) / sin a *(1+ cos a) =

sin ^2(a)/sin a * (1 + cos a)= sin a /(1 + cos a)= R.H.S.

this is standard method to solve such problem , otherwise you can solve as

2. as taking

sin a =p/h

cos a =b/h

cosec a= h/ p

cot =b /p

Answer 2

$coseca + cota \\ \\ = \frac{1}{sina} + \frac{cosa}{sina } \\ \\ = \frac{1 + cosa}{sina} \\ \\ = \frac{1 - {cos}^{2} a}{sina(1 - cosa)} \\ \\ = \frac{ {sin}^{2} a}{sina(1 - cosa)} \\ \\ = \frac{sina}{1 - cosa}$