Question

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

• A. 1
• B. 2
• C. 3

Answer 1

The correct option is A 1

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