tan0/1- cot0+ cot0/1-tan0= 1+sec0cosec0
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Yogita Ingle 5 years ago
LHS = tanO/(1-cotO) + cotO/(1-tanO)%7D%20%2B%20%5Cfrac%7Bcos%5E2O%7D%7BsinO(cosO-sinO)%7D%20%5C%5C%20%3D%20%5Cfrac%7Bsin%5E2O%7D%7BcosO(sinO-cosO)%7D%20-%20%5Cfrac%7Bcos%5E2O%7D%7BsinO(sinO-cosO)%7D%20%5C%5C%20%3D%20%5Cfrac%7Bsin%5E3O-cos%5E3O%7D%7BsinOcosO(sinO-cosO)%7D%20%5C%5C%20%3D%5Cfrac%7B(sinO-cosO)(sin%5E2O%2Bcos%5E2O%2BsinOcosO)%7D%7BsinOcosO(sinO-cosO)%7D%20%5C%5C%20%3D%20%5Cfrac%7B1%2BsinOcosO%7D%7BsinOcosO%7D%20%5C%5C)
=
= [1 +(1/cosecOsecO)]/[1/cosecOsecO]
=[(cosecOsecO+1)/cosecOsecO]*[cosecOsecO]
=cosecOsecO+1
=RHS
Hence proved
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