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3.Trigonometrical Ratios, Functions and Identities
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यदि $\cot x=-\frac{5}{12}$ हो और $x$ द्वितीय चतुर्थांश में स्थित हैं, तो अन्य पाँच त्रिकोणमितीय फलनों को ज्ञात कीजिए।
A
$\frac{13}{12}$
B
$\frac{13}{12}$
C
$\frac{13}{12}$
D
$\frac{13}{12}$
Solution
since $\cot x=-\frac{5}{12},$ we have $\tan x=-\frac{12}{5}$
Now $\sec ^{2} x=1+\tan ^{2} x=1+\frac{144}{25}=\frac{169}{25}$
Hence $\sec x=\pm \frac{13}{5}$
since $x$ lies in second quadrant, sec $x$ will be negative. Therefore
$\sec x=-\frac{13}{5}$
which also gives
$\cos x=-\frac{5}{13}$
Further, we have
$\sin x =\tan x \cos x=\left(-\frac{12}{5}\right) \times\left(-\frac{5}{13}\right)=\frac{12}{13} $
and $\cos ec\, x =\frac{1}{\sin x}=\frac{13}{12}$
Standard 11
Mathematics
