Question

sinx+sin3x/cosx+cos3x=tan2x
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Answer 1

i hope it will help u...

Answer 2

Answer:

tan2x

Step-by-step explanation:

Used Formulas -

1. SinC + SinD = 2sin(C+D/2) Cos(C - D/2)

2. CosC + CosD = 2Cos(C + D/2) Cos(C-D/2)

3. Sinx /cosx = tanx

LHS=

$\bf \: \frac{sinx + sin3x}{cosx + cos3x}$

$= \bf \: \frac{2sin \left( \frac{x + 3x}{2} \right) \: cos \left( \frac{x - 3x}{2} \right)}{2cos \left( \frac{x + 3x}{2} \right)cos\left( \frac{x - 3x}{2} \right)}$

$= \bf \: \frac{sin\left( \frac{x + 3x}{2} \right)}{cos\left( \frac{x + 3x}{2} \right)} \\ \\ \bf \: = \frac{sin2x}{cos2x} \\ \\ = \bf \: tan2x$