सीमा का मान ज्ञात कीजिए: $\mathop {\text{Limit}}\limits_{x \to 4} \frac{(\cos \alpha)^x - (\sin \alpha)^x - \cos 2\alpha}{x - 4}$,जहाँ $0 < \alpha < \frac{\pi}{2}$.
- A$(\cos \alpha)^4 \ln(\cos \alpha) + (\sin \alpha)^4 \ln(\sin \alpha)$
- B$-(\cos \alpha)^4 \ln(\cos \alpha) - (\sin \alpha)^4 \ln(\sin \alpha)$
- C$(\cos \alpha)^4 \ln(\cos \alpha) - (\sin \alpha)^4 \ln(\sin \alpha)$
- D$-(\cos \alpha)^4 \ln(\cos \alpha) + (\sin \alpha)^4 \ln(\sin \alpha)$
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Difficult
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$\mathop {\lim }\limits_{x \to \pi /2} \left[ {x\tan x - \left( {\frac{\pi }{2}} \right)\sec x} \right] = $
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View Solution$\lim _{x \rightarrow 1}\left((1-x) \tan \left(\frac{\pi x}{2}\right)\right)=$
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