The period of sin ⁡x cos ⁡3x+ sin ⁡3x cos ⁡9x+ sin ⁡9x cos ⁡27x+ sin ⁡27x cos ⁡81x is

Question

Accepted Answer

Correct answer: D. (d) Given, sin ⁡x cos ⁡3x+ sin ⁡3x cos ⁡9x+ sin ⁡9x cos ⁡27x+ sin ⁡27x cos ⁡81x Multiply and divide by 2 . = 12( 2 sin ⁡ xcos ⁡x cos ⁡3 xcos ⁡x+ 2 sin ⁡3 xcos ⁡3x cos ⁡9 xcos ⁡3x+) sin ⁡9 xcos ⁡9x cos ⁡27 xcos ⁡9x (+ 2 sin ⁡27 xcos ⁡27x cos ⁡81 xcos ⁡27x) = 12( sin ⁡2x cos ⁡3 xcos ⁡x+ sin ⁡6x cos ⁡9 xcos ⁡3x+ sin ⁡18x cos ⁡27 xcos ⁡9x) (+ sin ⁡54x cos ⁡81 xcos ⁡28x) i.e. 2x=3x-x = 12( sin ⁡ (3x-x ) cos ⁡3 xcos ⁡x+ sin ⁡ (9x-3x ) cos ⁡9 xcos ⁡3x+ sin ⁡ (27x-9x ) cos ⁡27 xcos ⁡9x) (+ sin ⁡ (81x-27x ) cos ⁡81 xcos ⁡27x) = 12 [ tan ⁡3x- tan ⁡x+ tan ⁡9x- tan ⁡3x+ tan ⁡27x = 12 [ tan ⁡ (81x )- tan ⁡x ] ∴ Required period is .

$The period of \frac{sin x}{cos 3 x} + \frac{sin 3 x}{cos 9 x} + \frac{sin 9 x}{cos 27 x} + \frac{sin 27 x}{cos 81 x} is$

Solution

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