If fn(x)=sin⁡xcos⁡3x+sin⁡3xcos⁡32x+sin⁡32xcos⁡33x+….+sin⁡3n−1xcos⁡3nx Then f2(π/4)+f3(π/4)=______

f2(x)+f3(x)=12(tan⁡9x−tan⁡x)+12(tan⁡27x−tan⁡x)⇒f2(π/4)+f3(π/4)=12(1−1)+12(−1−1)=−1

If fn(x)=sin⁡xcos⁡3x+sin⁡3xcos⁡32x+sin⁡32xcos⁡33x+….+sin⁡3n−1xcos⁡3nx Then f2(π/4)+f3(π/4)=______

f2(x)+f3(x)=12(tan⁡9x−tan⁡x)+12(tan⁡27x−tan⁡x)⇒f2(π/4)+f3(π/4)=12(1−1)+12(−1−1)=−1

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If $f_{n} (x) = \frac{\sin x}{\cos 3 x} + \frac{\sin 3 x}{\cos 3^{2} x} + \frac{\sin 3^{2} x}{\cos 3^{3} x} + \dots . + \frac{\sin 3^{n - 1} x}{\cos 3^{n} x} Then f_{2} (π / 4) + f_{3} (π / 4) =______$

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$\begin{array}{l} f_{2} (x) + f_{3} (x) = \frac{1}{2} (\tan 9 x - \tan x) + \frac{1}{2} (\tan 27 x - \tan x) \\ \Rightarrow f_{2} (π / 4) + f_{3} (π / 4) = \frac{1}{2} (1 - 1) + \frac{1}{2} (- 1 - 1) = - 1 \end{array}$

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If fn(x)=sin⁡xcos⁡3x+sin⁡3xcos⁡32x+sin⁡32xcos⁡33x+….+sin⁡3n−1xcos⁡3nx Then f2(π/4)+f3(π/4)=______

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If $f_{n} (x) = \frac{\sin x}{\cos 3 x} + \frac{\sin 3 x}{\cos 3^{2} x} + \frac{\sin 3^{2} x}{\cos 3^{3} x} + \dots . + \frac{\sin 3^{n - 1} x}{\cos 3^{n} x} Then f_{2} (π / 4) + f_{3} (π / 4) =______$