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3.Trigonometrical Ratios, Functions and Identities
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જો $\tan \theta + \sec \theta = {e^x},$ તો $\cos \theta $ =
A
$\frac{{({e^x} + {e^{ - x}})}}{2}$
B
$\frac{2}{{({e^x} + {e^{ - x}})}}$
C
$\frac{{({e^x} - {e^{ - x}})}}{2}$
D
$\frac{{({e^x} - {e^{ - x}})}}{{({e^x} + {e^{ - x}})}}$
Solution
(b) $\tan \theta + \sec \theta = {e^x}$…..$(i)$
$\therefore \,\,\,\sec \theta – \tan \theta = {e^{ – x}}$…..$(ii)$
From $(i)$ and $(ii),$
$\,2\sec \theta = {e^x} + {e^{ – x}}\,$
$\Rightarrow \,\cos \theta = \frac{2}{{{e^x} + {e^{ – x}}}}.$
Standard 11
Mathematics
