Maharashtra State BoardHSC Arts 12th Board Exam
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In ∆ABC, prove that cos2Aa2-cos2cc2=1a2-1c2 - Mathematics and Statistics

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Sum

In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`

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Solution

Consider L.H.S. = `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2`

= `(1 - 2sin^2 "A")/"a"^2 - (1 - 2sin^2"C")/"c"^2`

= `1/"a"^2 - 2  (sin^2"A")/"a"^2 - 1/"c"^2 + 2  (sin^2"C")/"c"^2`

= `1/"a"^2 - 2"k"^2 - 1/"c"^2 + 2"k"^2`  .......[By since rule]

= `1/"a"^2 - 1/"c"^2`

= R.H.S.

Concept: Solutions of Triangle
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