In a `Delta A B C ,` prove the following : `a^2=(b+c)^2-4bc cos^2(A/2)dot`

Explanation

RHS `=(b+c)^{2}-4 b c \cos ^{2} \frac{A}{2}`
`=b^{2}+c^{2}+2 b c-4 b c\(\frac{\cos A+1}{2})`
`=b^{2}+c^{2}+2 b c-2 b c(\cos A+1)`
`=b^{2}+c^{2}-2 b c \cdot \frac{b^{2}+c^{2}-a^{2}}{2 b c}`
`=b^{2}+c^{2}-(b^{2}+c^{2}-a^{2})`
`=b^{2}+c^{2}-b^{2}-c^{2}+a^{2}`
`=a^{2}=` LHS


`\So,` LHS = RHS