Given two functions fx and gx such that fx - sin arctan x- gx -tan arcsin x- and 0- x - -2- The value of the composite function f g -10 is-

The correct option is A 0.314 g(x)=tan (sin ^ 1 x ) =tanθ #160; = x √( 1 x ^ 2 ) #160; f(x)=sin (tan ^ 1 x ) = x √( 1+ x ^ 2 ) ...

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Standard XII

Mathematics

Basic Trigonometric Identities

Given two fun...

Question

Given two functions $f (x)$ and $g (x)$ such that $f (x) = sin (a r c t a n x), g (x) = tan (a r c sin x)$ , and $0 \leq x < \frac{π}{2}$ . The value of the composite function $f (g (\frac{π}{10}))$ is:

0.314

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0.354

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0.577

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0.707

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0.866

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Solution

The correct option is A $0.314$
$g (x) = tan ({sin}^{- 1} x) = tan θ$
$= \frac{x}{\sqrt{1 - x^{2}}}$
$f (x) = sin ({tan}^{- 1} x) = \frac{x}{\sqrt{1 + x^{2}}}$
$f (g (x)) = \frac{g (x)}{\sqrt{1 + {g (x)}^{2}}}$
$= \frac{\frac{x}{\sqrt{1 - x^{2}}}}{\sqrt{1 + \frac{x}{\sqrt{1 - x^{2}}}}} = x$
$f (g (\frac{π}{10})) = 0.314$

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Given two functions f(x) and g(x) such that f(x)=sin(arctanx),g(x)=tan(arcsinx), and 0≤x<π2. The value of the composite function f(g(π10)) is:

The correct option is A 0.314g(x)=tan(sin−1x)=tanθ=x√1−x2f(x)=sin(tan−1x)=x√1+x2f(g(x))=g(x)√1+g(x)2=x√1−x2√1+x√1−x2=xf(g(π10))=0.314

Given two functions $f (x)$ and $g (x)$ such that $f (x) = sin (a r c t a n x), g (x) = tan (a r c sin x)$ , and $0 \leq x < \frac{π}{2}$ . The value of the composite function $f (g (\frac{π}{10}))$ is: