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Maths-

General

Easy

Question

$fraction numerator d over denominator d x end fraction sin to the power of negative 1 end exponent invisible function application open parentheses x square root of 1 minus x end root plus square root of x square root of open 1 minus x squared close parentheses end root close$ is equal to

$- \frac{1}{2 x \sqrt{1 - x}} - \frac{1}{\sqrt{1 - x^{2}}}$
$\frac{1}{2 \sqrt{x} \sqrt{1 - x^{2}}} - \frac{1}{\sqrt{1 - x^{2}}}$
$\frac{1}{2 \sqrt{x} \sqrt{1 - x}} + \frac{1}{\sqrt{1 - x^{2}}}$
$- \frac{1}{2 \sqrt{x} \sqrt{1 - x}} + \frac{1}{\sqrt{1 - x^{2}}}$

The correct answer is: $fraction numerator 1 over denominator 2 square root of x square root of 1 minus x end root end fraction plus fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction$

Since, $sin to the power of negative 1 end exponent invisible function application open parentheses x square root of 1 minus x end root plus square root of x square root of 1 minus x squared end root close parentheses equals sin to the power of negative 1 end exponent invisible function application x plus$ $sin to the power of negative 1 end exponent invisible function application square root of x$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell therefore fraction numerator d over denominator d x end fraction open curly brackets sin to the power of negative 1 end exponent invisible function application open parentheses x square root of 1 minus x end root plus square root of x square root of 1 minus x squared end root close parentheses close curly brackets end cell row cell equals fraction numerator d over denominator d x end fraction open parentheses sin to the power of negative 1 end exponent invisible function application x plus sin to the power of negative 1 end exponent invisible function application square root of x close parentheses equals fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction plus fraction numerator 1 over denominator 2 square root of x square root of 1 minus x end root end fraction end cell end table$

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