Question

Let $y=f\left(x\right)$ and $f:R\circledR R$ be an odd function which is differentiable such that $f^{{}^{\prime }"}\left(x\right)>0$ and $f(a,b)=si{n}^{8}a+co{s}^{8}b+2-4si{n}^{2}aco{s}^{2}b$.
If $f^{\prime \prime }\left(f\right(a,b\left)\right)=0thensi{n}^{2}a+si{n}^{2}b=$

• A. 1
• B. 2
• C. 3

Answer 1

The correct option is A 1

$f"\left(x\right)$ is an odd function
$f(a,b)=0\Phi (si{n}^{4}a-1{)}^2+(co{s}^{4}b-1{)}^2+2(si{n}^{2}a-co{s}^{2}b{)}^2=0$
$\Rightarrow si{n}^2\alpha +si{n}^2\beta =1$