Explain tan 2x formula- - Tan2x-2tanx-1-tan2x -

[ Tan2x=2tanx/1 tan^2x ]DerivationTan2x=2tanx/1 tan^2x0ex0exAs per the addition formula.0ex0ex[ tan(a+b)=tana+tanb/1 tana.tanb ]0ex0exSo, for this let a = b , i ...

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Standard XIII

Mathematics

Conditional Identities

Explain tan 2...

Question

Explain $\tan 2 x$ formula.
$\begin{array}{l} T a n 2 x = \frac{2 t a n x}{1 - t a n^{2} x} \end{array}$

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Solution

$\begin{array}{l} T a n 2 x = \frac{2 t a n x}{1 - t a n^{2} x} \end{array}$
Derivation
$T a n 2 x = \frac{2 t a n x}{1 - t a n^{2} x} A s p e r t h e a d d i t i o n f o r m u l a . \begin{array}{l} t a n (a + b) = \frac{t a n a + t a n b}{1 - t a n a . t a n b} \end{array} S o, f o r t h i s l e t a = b, i t b e c o m e s \begin{array}{l} t a n (a + a) = \frac{t a n a + t a n a}{1 - t a n a . t a n a} \end{array} \begin{array}{l} T a n 2 a = \frac{2 t a n a}{1 - t a n^{2} a} \end{array}$
Hence, explained.

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Explain tan2x formula. Tan2x=2tanx1−tan2x

Tan2x=2tanx1−tan2xDerivationTan2x=2tanx1-tan2xAspertheadditionformula.tan(a+b)=tana+tanb1−tana.tanbSo,forthisleta=b,itbecomestan(a+a)=tana+tana1−tana.tanaTan2a=2tana1−tan2aHence, explained.

Explain $\tan 2 x$ formula.
$\begin{array}{l} T a n 2 x = \frac{2 t a n x}{1 - t a n^{2} x} \end{array}$