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Proof :
We have,
lim\(_{θ\to 0} { \dfrac {\mathrm tan \mathrm θ}{ \mathrm θ} } \) = lim\(_{θ\to 0} { \dfrac {\mathrm \sin \mathrm θ} {\mathrm θ \mathrm \cos\mathrm θ} } \) \( \{∵ \tan\theta = \dfrac {\sin\theta}{\cos\theta} \} \)
= lim\(_ \mathrm {θ\to 0} \dfrac {\mathrm{\sin θ} } { \mathrm θ} \) × lim\(_ \mathrm {θ\to 0} \mathrm{cos θ} \) \( \{ ∵\) lim\(_{x\to y}f(x)g(x)\) = lim\(_{x\to y}f(x)\) . lim\(_{x\to y}g(x) \} \)
= 1 × 1
= 1
Hence,
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