InterviewSolution
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InterviewSolution
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The most general solution of the equation sec2 x = \(\sqrt{2}\) (1 – tan2 x ) are given by (a) nπ ± \(\frac{π}{4}\)(b) 2nπ ± \(\frac{π}{4}\) (c) nπ ± \(\frac{π}{8}\)(d) None of these |
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Answer» Answer : (c) nπ ± \(\frac{\pi}{8}\) sec2 x = \(\sqrt{2}\) (1 - tan2 α) ⇒ tan2 α + 1 = \(\sqrt{2}\) (1 – tan2 α ) ⇒ tan2 α (1 + \(\sqrt{2}\) ) = \(\sqrt{2}\) – 1 ⇒ tan2 α = \(\frac{\sqrt{2} -1}{\sqrt{2} +1}\) = \(\frac{(\sqrt{2} -1)^2}{(\sqrt{2}+1)(\sqrt{2}-1)}\) = \((\sqrt{2}-1)^2\) = \({tan}^2\,\frac{\pi}{8}\) ∴ tan α = tan \(\big(± \frac{\pi}{8}\big)\) α = nπ ± \(\frac{\pi}{8}\) |
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