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Question

A right angled triangle has one leg of length 1 unit, another leg of length x units and hypotenuse is of length y units. The angle opposite to the side of length x units is θ. Then

A
y3x3=sec3θtan3θ
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B
limθπ/2(yx)=0
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C
limθπ/2(y2x2)=1
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D
limθπ/2(y3x3)=1
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Solution

The correct option is C limθπ/2(y2x2)=1

x=tanθ,y=secθ
y3x3=sec3θtan3θ

limθπ/2(secθtanθ)
=limθπ/21sinθcosθ=0

limθπ/2(sec2θtan2θ)=1

limθπ/2(sec3θtan3θ) does not exist.

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