Question

Prove the following:

$tan 4 straight x space equals space fraction numerator 4 tanx space left parenthesis 1 minus tan squared straight x right parenthesis over denominator 1 minus 6 tan squared straight x plus tan to the power of 4 straight x end fraction$

Solution

Using $WiredFaculty$ we get
$tan 4 straight x space equals space fraction numerator 2 tan 2 straight x over denominator 1 minus tan squared 2 straight x end fraction space equals space fraction numerator 2. begin display style fraction numerator 2 space tanx over denominator 1 minus tan squared straight x end fraction end style over denominator 1 minus open parentheses begin display style fraction numerator 2 space tanx over denominator 1 minus tan squared straight x end fraction end style close parentheses squared end fraction$
$rightwards double arrow$ $tan 4 straight x space equals space fraction numerator begin display style fraction numerator 2. space 2 tanx over denominator 1 minus tan squared straight x end fraction end style over denominator begin display style fraction numerator left parenthesis 1 minus tan squared straight x right parenthesis squared minus 4 tan squared straight x over denominator left parenthesis 1 minus tan squared straight x right parenthesis squared end fraction end style end fraction space equals space fraction numerator 2.2 tanx over denominator 1 minus tan squared straight x end fraction cross times fraction numerator left parenthesis 1 minus tan squared straight x right parenthesis squared over denominator 1 plus tan to the power of 4 straight x minus 2 tan squared straight x minus 4 tan squared straight x end fraction$
Hence, $WiredFaculty$

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Principle Of Mathematical Induction

Prove the following:

$tan 4 straight x space equals space fraction numerator 4 tanx space left parenthesis 1 minus tan squared straight x right parenthesis over denominator 1 minus 6 tan squared straight x plus tan to the power of 4 straight x end fraction$

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Find 1 radian angle in degrees, minutes, seconds.

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