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| 1. |
Prove that tan²A+cot²A+2=sec²A cosec²A |
| Answer» LHS {tex}= tan^2\xa0A + cot^2\xa0A + 2{/tex}{tex}= sec^2\xa0A - 1 + cosec^2\xa0A - 1 + 2{/tex}= sec2\xa0A + cosec2\xa0A{tex}=\\frac{1}{\\cos ^{2} A}+\\frac{1}{\\sin ^{2} A}{/tex}{tex}=\\frac{\\sin ^{2} A+\\cos ^{2} A}{\\cos ^{2} A \\cdot \\sin ^{2} A}{/tex}{tex}=\\frac{1}{\\cos ^{2} A \\cdot \\sin ^{2} A}{/tex}{tex}=\\frac{1}{\\cos ^{2} A} \\times \\frac{1}{\\sin ^{2} A}{/tex}= sec2 A. cosec2\xa0A = RHS | |