Question

Proove that: cosec A - cot A= √1-cos A/ 1+cos A

Answer 1

Answer :,

1) 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

where p,b,h are sides of a right angled triangle ,

p=perpendicular side

b=base of the triangle

h= hypotenuse

put these valve in L.H.S. and R.H.S. and hence prove L.H.S. = R.H.S. .

hope it will help