The value of tan-16 - 2tan-8 - 4 is equal to

The correct option is D π16 We know that,tan A =cot A 2cot 2A LHS=tanπ #160; 16 #160; +2tanπ #160; 8 #160; +4 =cotπ ...

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Sum of Trigonometric Ratios in Terms of Their Product

The value of ...

Question

The value of $tan \frac{π}{16} + 2 tan \frac{π}{8} + 4$ is equal to

cot \frac{π}{8}

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cot \frac{π}{16}

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cot \frac{π}{16} - 14

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none of these

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Solution

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\begin{matrix} {cos}^{4} \frac{π}{16} + {sin}^{4} \frac{π}{16} - {sin}^{2} \frac{π}{16} {cos}^{2} \frac{π}{16} + {cos}^{4} \frac{3 π}{16} + {sin}^{4} \frac{3 π}{16} - {sin}^{2} \frac{3 π}{16} {cos}^{2} \frac{3 π}{16} \end{matrix}

\int_{0}^{a^{2}} \frac{1}{1 + 16 x^{2}} d x = \frac{π}{16}

\int_{0}^{k} \frac{1}{2 + 8 x^{2}} d x = \frac{π}{16},

\int_{0}^{a^{2}} \frac{1}{1 + 16 x^{2}} d x = \frac{π}{16}

\frac{1}{5} [{tan}^{2} \frac{π}{16} + {tan}^{2} \frac{2 π}{16} + {tan}^{2} \frac{3 π}{13} + . . . + {tan}^{2} \frac{7 π}{16}]

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