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Which of the following trigonometric functions is an odd function?निम्नलिखित में से कौन-सा त्रिकोणमितीय फलन विषम फलन है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\tan x\)\(\tan x\)
\(\tan(-x)=\frac{\sin(-x)}{\cos(-x)}=\frac{-\sin x}{\cos x}=-\tan x\); therefore, \(\tan x\) is an odd function. \(\cos x\) and \(\sec x\) are even, and \(\cos^2 x\) is also even. Exam tip: test an odd function using \(f(-x)=-f(x)\).\(\tan(-x)=\frac{\sin(-x)}{\cos(-x)}=\frac{-\sin x}{\cos x}=-\tan x\), अतः \(\tan x\) विषम फलन है। \(\cos x\) और \(\sec x\) सम फलन हैं, क्योंकि इनके लिए \(f(-x)=f(x)\) होता है। \(\cos^2 x\) भी सम है। परीक्षा टिप: विषम फलन की जाँच के लिए \(f(-x)=-f(x)\) लगाएँ।
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