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in Mathematics by (52.5k points)

Prove that lim(θ0) sinθ/θ = 1 (q being in radians) and hence show that lim(θ 0) tanθ/θ = 1.

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Consider a circle with centre O and radius ‘r’ Mark two points A and B on the circle so that 

Join AB. Draw BM ⊥ OA 

From the figure it is clear that. 

Area of ∆OAB < Area of sector OAB < sector of ∆OAC …. (1) 

Area of ∆OAB = 1/2 OA.BM 

[In ∆OBM. Sin θ BM/r ⇒ BM = r Sinθ]

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