Question

period of sinx+sin2x/cosx+cos2x

Answer 1

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Answer 2

The value of period of  $\frac{sinx+sin2x}{cosx+cos2x}$   is $\frac{2\pi }{3}$.

Step-by-step explanation:

Given:

$\frac{sinx+sin2x}{cosx+cos2x}$

To Find:

The value of period of  $\frac{sinx+sin2x}{cosx+cos2x}$ .

Formula Used:

Sos A + Cos B = 2 Cos(A+B)/2 . Cos(A-B)/2

Solution:

As given-  $\frac{sinx+sin2x}{cosx+cos2x}$.

$\frac{sinx+sin2x}{cosx+cos2x}$

$=\frac{2sin\frac{(x+2x)}{2} cos\frac{(x-2x)}{2} }{ 2cos\frac{(x+2x)}{2} cos\frac{(x-2x)}{2} }$

$=\frac{2sin\frac{3x}{2} cos\frac{x}{2} }{ 2cos\frac{3x}{2} cos\frac{x}{2} }$

$= \frac{sin\frac{3x}{2} }{cos\frac{3x}{2} }$

$= tan\frac{3x}{2}$

The period of tan ax  is  $\frac{\pi }{a}$.

Hence, the period of $tan\frac{3x}{2}$  will be   $=\frac{\pi }{(\frac{3}{2}) }$  

                                                           $=\frac{2\pi }{3 }$

Thus, the value of period of  $\frac{sinx+sin2x}{cosx+cos2x}$   is $\frac{2\pi }{3}$.

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