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Prove that: (cosecA – secA) (cotA – tanA) = (cosecA + secA) (secA cosecA – 2)

Prove that:
(cosecA – secA) (cotA – tanA) = (cosecA + secA) (secA cosecA – 2)

Grade:12

2 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
RHS=cosecA+secA)(secAcosecA-2)
=(1/sinA+1/cosA){(1/cosA)(1/sinA)-2}
=[(cosA+sinA)/(sinAcosA) ][(1-2sinAcosA)/(sinAcosA)]
=[(cosA+sinA)/(sinAcosA)][(cosA-sinA)2/(sinAcosA)]
=(cosA+sinA)(cosA-sinA)2/(sin2Acos2A)
=(cosA+sinA)(cosA-sinA)(cosA-sinA)/sin2Acos2A
=cos2A(cosA-sinA)/cos2Asin2A
LHS=(cosecA-secA)(cotA-tanA)
=(1/sinA-1/cosA)(cosA/sinA -sinA/cosA)
=(cosA-sinA/sinAcosA)(cos2A-sin2A)/sinAcosA
=(cosA-sinA)cos2A/sin2Acos2A
Thus LHS=RHS Hence Proved.
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
Aniket Pathak
18 Points
9 years ago
Thank you so much.....!

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