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General

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Question

$text If end text x comma y comma z text are in AP, then end text fraction numerator s i n invisible function application x minus s i n invisible function application z over denominator c o s invisible function application z minus c o s invisible function application x end fraction text is equal to end text$

$tan y$
$c o t y$
sin y
cos y

The correct answer is: $c o t invisible function application y$

Given x, y, z are in AP ⇒ 2y = x + z. Now
$fraction numerator s i n invisible function application x minus s i n invisible function application z over denominator c o s invisible function application z minus c o s invisible function application x end fraction equals fraction numerator 2 c o s invisible function application fraction numerator x plus z over denominator 2 end fraction times s i n invisible function application fraction numerator x minus z over denominator 2 end fraction over denominator 2 s i n invisible function application fraction numerator x plus z over denominator 2 end fraction times s i n invisible function application fraction numerator x minus z over denominator 2 end fraction end fraction equals c o t invisible function application y$

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$s i n invisible function application fraction numerator pi over denominator 9 end fraction s i n invisible function application fraction numerator 2 pi over denominator 9 end fraction s i n invisible function application fraction numerator 4 pi over denominator 9 end fraction s i n invisible function application fraction numerator pi over denominator 3 end fraction text is equal to end text$

$s i n invisible function application fraction numerator pi over denominator 9 end fraction s i n invisible function application fraction numerator 2 pi over denominator 9 end fraction s i n invisible function application fraction numerator 4 pi over denominator 9 end fraction s i n invisible function application fraction numerator pi over denominator 3 end fraction text is equal to end text$

Cadmium rods are used in a nuclear reactor for

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