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Prove that:tan t + 2cos t x cosec t = sec t x cosec t + cot t |
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Answer» \(tan\, t + 2cos \,t \; cosec \, t\) \(= \frac {sin\,t}{cos\,t }+ \frac{2cos\,t}{sin\,t}\) \(= \frac{sin^2t+ 2cos^2t}{sin\,t \;cos\,t}\) \(= \frac{1+ cos^2t}{sin\,t \;cos\,t}\) \((\because sin^2t + cos^2 t = 1)\) \(= sec\,t . cosec\,t + \frac{cos\,t}{sin\,t}\) \(= sec\, t . cosec.t + cot\,t\) Hence Proved. |
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