If a=tan⁡27θ−tan⁡θ and b=sin⁡θcos⁡3θ+sin⁡3θcos⁡9θ+sin⁡9θcos⁡27θ, then

# If $a=\mathrm{tan}27\theta -\mathrm{tan}\theta$ and $b=\frac{\mathrm{sin}\theta }{\mathrm{cos}3\theta }+\frac{\mathrm{sin}3\theta }{\mathrm{cos}9\theta }+\frac{\mathrm{sin}9\theta }{\mathrm{cos}27\theta },$ then

1. A

$a=b$

2. B

$a=2b$

3. C

$b=2a$

4. D

$a+b=2$

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### Solution:

We have,

$a=\mathrm{tan}27\theta -\mathrm{tan}\theta$

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