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May get help proving this one.

May get help proving this one.

Question Image
Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
put a-x =t and we get
L = lim_{t\rightarrow\infty}t\times tan(\pi/2 - \pi t/2a) = lim_{t\rightarrow\infty}t\times cot( \pi t/2a)
now by writing cot in terms of sin and cos we can just take out the cos as cos(0) = 1, and hence what remains is
L = lim_{t\rightarrow\infty}\frac{t}{sin(\pi t/2a)} = (2a/\pi)lim_{t\rightarrow\infty}\frac{\pi t/2a}{sin(\pi t/2a)}
and we know that the form oflimit x/sin(x) as x->0 is 1
hence proved
L = (2a/\pi)

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