In - ABC prove that a-b2cos2C-2-a-b2sin2C-2- c2

Expanding L.H.S.= (a^2+b^2 2ab)cos^2C/2+(a^2+b^2+2ab)sin^2C/2 =a^2+b^2+2ab ( sin^2C/2 cos^2C/2) =a^2+b^2 2ab cos C =a^2+b^2 (a^2+b^2 c^2)= ...

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Definition of a Determinant

In Δ ABC pr...

Question

In $Δ A B C$ prove that $(a - b)^{2} {cos}^{2} \frac{C}{2} + (a + b)^{2} {sin}^{2} \frac{C}{2} = c^{2}$

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{(a - b)}^{2} {cos}^{2} \frac{C}{2} + {(a + b)}^{2} {sin}^{2} \frac{C}{2} = c^{2}

△ A B C

(a - b)^{2} {cos}^{2} (\frac{C}{2}) + (a + b)^{2} {sin}^{2} (\frac{C}{2}) = c^{2}

Δ A B C,

(a - b)^{2} {cos}^{2} \frac{C}{2} + (a + b)^{2} {sin}^{2} \frac{C}{2}

Δ A B C

(a - b)^{2} {cos}^{2} (c / 2) + (a + b)^{2}

{sin}^{2} (c / 2) = c^{2}

Δ A B C

a - b^{2} {cos}^{2} \frac{c}{2} + a + b^{2} {sin}^{2} \frac{c}{2}

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