Let y - f x - f - R - R be an odd differentiable function such that f - x -0 and g - -sin 8-cos 8-2-4 sin 2-cos 2- Iff - g - -0- then sin 2-sin 2- is equal toA- 1B- 2C- 3D- 0

The correct option is A 1 f”(x) is odd function ⇒ g(α,β)=0 ⇒ (sin^4α 1)^2+(cos^4β 1)^2+2(sin^2 α cos^2 β)^2=0 sin^2 α+sin^2 β =1 ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Allied Angles

Let y = f x ,...

Question

Let $y = f (x)$ , $f : R \to R$ be an odd differentiable function such that $f^{'''} (x) > 0$ and $g (α, β) = s i n^{8} α + c o s^{8} β + 2 - 4 s i n^{2} α c o s^{2} β$ . If $f^{''} (g (α, β)) = 0$ , then $s i n^{2} α + s i n^{2} β$ is equal to

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Solution

The correct option is B
1

$f^{''} (x)$ is odd function $\Rightarrow g (α, β) = 0$

$\Rightarrow (s i n^{4} α - 1)^{2} + (c o s^{4} β - 1)^{2} + 2 (s i n^{2} α - c o s^{2} β)^{2} = 0$

$s i n^{2} α + s i n^{2} β = 1$

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Q. 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)

= s i n^{8} a + c o s^{8} b + 2 - 4 s i n^{2} a c o s^{2} b

.
If f'' (f(a,b))=0 then

s i n^{2} a + s i n^{2} b =

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f^{''} (f (a, b)) = 0 t h e n s i n^{2} a + s i n^{2} b =

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Let y=f(x), f:R→R be an odd differentiable function such that f′′′(x)>0 and g(α,β)=sin8α+cos8β+2−4sin2αcos2β. If f′′(g(α,β))=0, then sin2α+sin2β is equal to

The correct option is B 1 f′′(x) is odd function ⇒g(α,β)=0 ⇒(sin4α−1)2+(cos4β−1)2+2(sin2α−cos2β)2=0 sin2α+sin2β=1

Let $y = f (x)$ , $f : R \to R$ be an odd differentiable function such that $f^{'''} (x) > 0$ and $g (α, β) = s i n^{8} α + c o s^{8} β + 2 - 4 s i n^{2} α c o s^{2} β$ . If $f^{''} (g (α, β)) = 0$ , then $s i n^{2} α + s i n^{2} β$ is equal to

The correct option is B
1

$f^{''} (x)$ is odd function $\Rightarrow g (α, β) = 0$

$\Rightarrow (s i n^{4} α - 1)^{2} + (c o s^{4} β - 1)^{2} + 2 (s i n^{2} α - c o s^{2} β)^{2} = 0$

$s i n^{2} α + s i n^{2} β = 1$