The value of tan-7-tan2 -7-tan3 -7-tan4 -7-tan5 -7-tan6 -7-tan7 -7-

Tanπ7+tan2π7+tan3π7+tan4π7+tan5π7 +tan6π7+tan7π7 =(tanπ7+tan6π7)+(tan2π7+tan5π7) +(tan3π7+tan4π7)+tanπ =(tanπ7 tanπ7)+(tan2π7 tan2π7) +(tan3π7 tan3π7)+0 =0 ...

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Standard XII

Mathematics

Trigonometric Ratios of Allied Angles

The value of ...

Question

The value of $tan \frac{π}{7} + tan \frac{2 π}{7} + tan \frac{3 π}{7} + tan \frac{4 π}{7} + tan \frac{5 π}{7} + tan \frac{6 π}{7} + tan \frac{7 π}{7} =$

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Solution

$tan \frac{π}{7} + tan \frac{2 π}{7} + tan \frac{3 π}{7} + tan \frac{4 π}{7} + tan \frac{5 π}{7} + tan \frac{6 π}{7} + tan \frac{7 π}{7}$

$= (tan \frac{π}{7} + tan \frac{6 π}{7}) + (tan \frac{2 π}{7} + tan \frac{5 π}{7}) + (tan \frac{3 π}{7} + tan \frac{4 π}{7}) + tan π$

$= (tan \frac{π}{7} - tan \frac{π}{7}) + (tan \frac{2 π}{7} - tan \frac{2 π}{7}) + (tan \frac{3 π}{7} - tan \frac{3 π}{7}) + 0$

$= 0$

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Similar questions

Q. The value of

{tan}^{2} \frac{π}{7} + {tan}^{2} \frac{2 π}{7} + {tan}^{2} \frac{3 π}{7}

Q. The value of

\frac{tan^{2} \frac{π}{7} + tan^{2} \frac{2 π}{7} + tan^{2} \frac{3 π}{7}}{cot^{2} \frac{π}{7} + cot^{2} \frac{2 π}{7} + cot^{2} \frac{3 π}{7}}

tan \frac{π}{11} + tan \frac{2 π}{11} + tan \frac{4 π}{11} + tan \frac{7 π}{11} + tan \frac{9 π}{11} + tan \frac{10 π}{11}

Q. Find the sum of digits of the numerical value of

({tan}^{2} \frac{π}{7} + {tan}^{2} \frac{2 π}{7} + {tan}^{2} \frac{3 π}{7}) ({cot}^{2} \frac{π}{7} + {cot}^{2} \frac{2 π}{7} + {cot}^{2} \frac{3 π}{7})

Q. Solve

tan \frac{π}{16} + tan \frac{3 π}{16} + tan \frac{5 π}{16} + tan \frac{7 π}{16}

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Trigonometric Ratios of Allied Angles

Standard XII Mathematics

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The value of tanπ7+tan2π7+tan3π7+tan4π7+tan5π7+tan6π7+tan7π7=

tanπ7+tan2π7+tan3π7+tan4π7+tan5π7+tan6π7+tan7π7 =(tanπ7+tan6π7)+(tan2π7+tan5π7)+(tan3π7+tan4π7)+tanπ =(tanπ7−tanπ7)+(tan2π7−tan2π7)+(tan3π7−tan3π7)+0 =0

The value of $tan \frac{π}{7} + tan \frac{2 π}{7} + tan \frac{3 π}{7} + tan \frac{4 π}{7} + tan \frac{5 π}{7} + tan \frac{6 π}{7} + tan \frac{7 π}{7} =$