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If 2x = Sec A and \(\frac{2}{x}\) = tanA, then find (x2 − \(\frac{1}{x^2}\)). |
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Answer» Given that, 2x = Sec A and 2/x = tanA Therefore, sec2A = 4x2 and tan2A = \(\frac{4}{x^2}\) We know that, sec2A – tan2A = 1. Therefore, 4x2 − \(\frac{4}{x^2}\) = 1 (By putting values of sec2A and tan2A) ⇒ 4(x2 - \(\frac{1}{x^2}\)) = 1 ⇒ x2 - \(\frac{1}{x^2}\) = \(\frac{1}{4}\). Hence, The value of x2 - \(\frac{1}{x^2}\) is \(\frac{1}{4}\). |
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