Question

(1
cosec A- cotA
sin
1 +COSA​

Answer 1

Answer:

LHS = (1 + cos A)/ (1 - cos A)

RHS = tan²A/(secA - 1)²

= [tanA/(sec-1)]^2

= [tanA/((1/cosA)-1)]^2

= [tanA/(1-cosA)/cosA]^2

= [(tanA*cosA)/(1-cosA)]^2

= [sinA/(1-cosA)]^2

= sinA^2/(1-cosA)^2

= (1-cosA^2)/(1-cosA)^2

= [(1-cosA)*(1+cosA)]/[(1-cosA)*(1-cosA)]

= (1+cosA)/(1-cosA)

Answer 2

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.

Step-by-step explanation: