Question

if f(x)=2x√1-x² then show that f(sin x/2)=sin x Its a maths question from Isc 11th book

Answer 1

Step-by-step explanation:

This is the answer

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Answer 2

Formula to remember -

$Sin^2x/2 +Cos^2x/2 = 1$

$Cos\frac{x}{2} = \sqrt{1-Sin^2\frac{x}{2} }$

$2Sin\frac{x}{2} Cos\frac{x}{2} = Sinx$

Step-by-step explanation:

Given - f(x)=2x√1-x²

Now puttin x = Sinx/2 in the function we get,

⇒  $f(Sin\frac{x}{2} ) = 2 Sin\frac{x}{2} \sqrt{1-sin^2\frac{x}{2} }$

⇒   $f(Sin\frac{x}{2} ) = 2Sinx\frac{x}{2} Cos\frac{x}{2}$

⇒   $f(Sin\frac{x}{2} ) = Sinx$

Hence, RHS = LHS

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