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Asked by jatinsisodia2325 | 18 Mar, 2024, 12:33: PM
answered-by-expert Expert Answer

Qn.# 50

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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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img

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Qn. 51

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

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Qn. 52

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Let x-a = θ

img

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

if  x → a , then θ→0

Hence  ( cosθ sin(a) - sin(a) ) → 0

Hence eqn.(1) is written as

img

Hence we get the limit as

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