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| 1. |
Cot theta+cosec theta-1/cot theta-cosec theta+1 |
| Answer» (cotA+cosecA-1)/(cotA-cosecA+1)=(cotA+cosecA-1)²/(cotA+cosecA-1)(cotA-cosecA+1)=(Cot²A+cosec²A+1+2cotAcosecA-2cotA-2cosecA)/(cot²A-cosec²A-1+2cosecA)={2cosec²A-2cosecA+2cotA(cosecA-1)}/(2cosecA-2)={2cosecA(cosecA-1)+2cotA(cosecA-1)}/2(cosecA-1)=2(cosecA-1)(cosecA+cotA)/2(cosecA-1)=cosecA+cotA | |