HSC Arts 12th Board ExamMaharashtra State Board
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In Δ ABC with the usual notations prove that (a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2 - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

In Δ ABC with the usual notations prove that `(a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2`

Solution

LHS= `(a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)`

`=a^2[cos^2(C/2)+sin^2(C/2)]+b^2[cos^2(C/2)+sin^2(C/2)]-2ab[cos^2(C/2)-sin^2(C/2)]`

`=a^2+b^2-a^2-b^2+c^2`

`=c^2`

=RHS

Hence proved

 

  Is there an error in this question or solution?

APPEARS IN

 2015-2016 (March) (with solutions)
Question 2.2.1 | 4.00 marks
Solution In Δ ABC with the usual notations prove that (a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2 Concept: Trigonometric Functions - Solution of a Triangle.
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