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X=cot theta+tan theta y=sec theta-cos theta then (x^2y) ^2/3-(xy^2) ^2/3= |
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Answer» The question should be: prove that (X 2 y) 2
−(XY 2 ) 3 2
=1 cotθ+tanθ= tanθ 1+tan 2 θ
= tanθ sec 2 θ
⇒x=cotθ+tanθ= sinθcosθ 1
secθ−cosθ= cosθ 1cos 2 θ
= cosθ sin 2 θ
⇒y=secθ−cosθ= cosθ sin 2 θ
∴x 2 = sin 2 θcos 2 θ 1
,y 2 = cos 2 θ sin 4 θ
∴x 2 y= sin 2 θcos 2 θ 1
× cosθ sin 2 θ
=sec 3 θ ∴xy 2 = sinθcosθ 1
× cos 2 θ sin 4 θ
=tan 3 θ ∴(x 2 y) 3 2
−(xy 2 ) 3 2
=(sec 3 θ) 3 2
−(tan 3 θ) 3 2
=sec 2 θ−tan 2 θ =1 |
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