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1). 02). -13). 14). 2 |
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Answer» secθ $( = \sqrt {2 + \sqrt {2 + \sqrt {2 +\ldots\ldots\ldots\ldots \INFTY } } } )$ ∴ secθ = $(\sqrt {2 + {\RM{sec\theta }}} )$ sec2θ = 2 + secθ sec2θ - secθ - 2 = 0 secθ $(= \frac{{1 \pm \sqrt {1 + 8} }}{2})$ secθ $( = \frac{{1 \pm 3}}{2})$ ∴ secθ = 2, -1 [secθ = -1 not possible] ∴ θ = 60° for 0 < θ <$(\frac{{\rm{\PI }}}{2})$ cosθ (1 +2cosθ) = cos60°(1 +2×cos60°) ∴ $( = \frac{1}{2}\left\{ {1 + 2 \times \frac{1}{2}} \RIGHT\} = 1)$ Shortcut: - Secθ = 2 Cosθ $( = \frac{1}{2})$ ∴ θ = 60° cos60° (1 + 2 cos60°) $( = \frac{1}{2}\left\{ {1 + 2 \times \frac{1}{2}} \right\})$ = 1 |
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