Question

what is the formula of tan 2A​

Answer 1

tan 2 A = 2 tan A/ 1-tan square a

Answer 2

Hey there,

If by chance you don't remember the formula, then use the following method.

What we know :-

$sin (2A)=2sinAcos A$

$cos 2A= cos^2A-sin^2A$

$Tan A =\frac{sinA}{cos A}$

$cot A =\frac{cosA}{sinA}= \frac{1}{tanA}$

What we need to find :-

$Tan 2A=?$

Procedure:-

Let us divide the first two given values to get $Cot 2A$ (as per fourth given).

$cot 2A=\frac{cos^2A-sin^2A}{2sinAcosA}$

         $=\frac{1}{2} (cot A-tanA)\\=\frac{1}{2} (\frac{1}{tanA} -tanA)\\=\frac{1}{2}(\frac{1-tan^2A}{tanA} )\\=\frac{1-tan^2A}{2tanA}$

$\frac{1}{cot2A} =tan2A=\frac{2tanA}{1-tan^2A}$

QED

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