Question

Let $a,b$ and $\angle A$ are known & $c_1,c_2$ are two values of c,then value of $c_1^2+c_2^2-2c_1{c}_2\cos 2A$ is equal to

• A. $a^2{\sin }^{2}A$
• B. $a^2{\cos }^{2}A$
• C. $2(a^2+b^2)$
• D. $4a^2{\cos }^{2}A$

Answer 1

The correct option is D $4a^2{\cos }^{2}A$

$c_1$ and $c_2$ are roots of equation,
So, $c_1+c_2=2bcosA{c}_1{c}_2=b^2-a^{2}So,c_1^2+c_2^2-2c_1{c}_2\cos 2A=(c_1+c_2{)}^2-2c_1{c}_2(1+\cos 2A)4b^2{\cos }^{2}A-2(b^2-a^2\left)\right(2{\cos }^{2}A)=4a^2{\cos }^{2}A$