JEE Class main Answered

Qn.# 50

Numerator is written as

(1-cos2x) = 2 sin²x

Denominator is written as

cos2x-cos8x = cos(5x-3x) - cos(5x+3x) = 2 sin5x sin3x

Hence eqn.(1) is written as

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Qn. 51

Let  (π/2)-x = θ , hence if (π/2)→x , then θ→0

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Qn. 52

Let x-a = θ

....................(1)

if  x → a , then θ→0

Hence  ( cosθ sin(a) - sin(a) ) → 0

Hence eqn.(1) is written as

Hence we get the limit as

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