Question

prove the following identities:
1)cosecA(1+cosA)(cosecA-cotA)=1
2)(1+tan2A)cotA=1
cosec2A
3)(secA-cosA)(secA+cosA)=sin2A+tan2A
4)cosecA+cotA=1/cosecA-cotA

Answer 1

As converting value of cosecA:-
CosecA + cosA (1/sinA) (cosecA-cotA)
=cosecA+ cosA/sinA (cosecA-cotA)
Putting value of cosA/sinA = cotA
=(cosecA+cotA) (cosecA-cotA)
Using identity a2-b2=(a+b)(a-b)
Cosec2A - Cot2A
Using identity Cosec2A-Cot2A=1
H.P.