Plz help me prove the foloowing trigonometric identities

Asked by sanheeta | 31st Aug, 2009, 10:27: PM

Expert Answer:

1/ LHS = (cosecA + sinA)(cosecA - sinA)

= (1/sinA + sinA)(1/sinA - sinA)

= [(1 + sin2A)/sinA][(1 - sin2A)/sinA]

= (1 + sin2A)(1 - sin2A)/sin2A

= (1 + sin2A)(cos2A)/sin2A

= cos2A/sin2A + cos2A

= cot2A + cos2A = RHS

2/LHS = secA(1 - sinA)(secA + tanA)

= (secA - secAsinA)(secA + tanA)

= (secA - tanA)(secA + tanA)

= sec2A - tan2A

= sec2A - sec2Asin2A

= sec2A(1 -  sin2A)

= sec2A cos2A

= 1 = RHS.

Regards,

Team,

TopperLearning.

Answered by  | 31st Aug, 2009, 10:52: PM

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