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प्रश्न
If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
विकल्प
3/4
1/2
2
5/4
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उत्तर
3/4
We have:
\[\tan x = \frac{1}{\sqrt{7}}\]
\[ \therefore \tan^2 x = \frac{1}{7}\]
Now, dividing the numerator and the denominator of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\text{ by }{cosec}^2 x:\]
\[\frac{1 - \tan^2 x}{1 + \tan^2 x}\]
\[ = \frac{1 - \frac{1}{7}}{1 + \frac{1}{7}}\]
\[ = \frac{6}{8} = \frac{3}{4}\]
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