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In A B C , prove that (a – b)^2 cos^2 C...

In ` A B C ,` prove that `(a – b)^2 cos^2 C/2 + (a + b)^2 sin^2 C/2 =c^2dot`

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Given, `(a – b)^2 cos^2 C/2 + (a + b)^2 sin^2 C/2`
We have to prove that `(a-(b^2cos^C/2)+(a+b)^2sin^2(C)/(2)=c^2dot`
Taking LHS
= `(a^2 + b^2 – 2ab) cos^2 C/2 + (a^2 + b^2 + 2ab) sin^2 C/2`
= `(a^2 + b^2)(cos^2 C/2 + sin^2 C/2) – 2ab(cos^2 C/2 – sin^2 C/2)`
...
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