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Prove that sin pi/14* sin 3pi/14* sin 5...

Prove that `sin pi/14* sin 3pi/14* sin 5pi/14`........... to 7 factors and `1/2^(6)`..

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that cos theta* cos 2theta* cos2^(2)theta * cos2^(3)theta x... ...

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  2. Prove that cos pi/15 * cos 2pi/15* cos3pi/15... . . to 7 factors = 1...

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  3. Prove that sin pi/14* sin 3pi/14* sin 5pi/14........... to 7 factors ...

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  4. If A gt 0, B gt 0 and A + B = pi/3 then find the maximum value of tan...

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  5. Find the minimum value of 9tan^(2)theta + 4cot^(2)theta.

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  6. Show that the maximum and minimum values of sqrt(a^(2)cos^(2)theta + ...

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  7. Find the set of possible values of (tan(x + pi/6))/tan x where x is an...

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  8. Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi...

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  9. Show that (sec^(2)theta - tan theta)/(sec^(2)+ tan theta) lies betwe...

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  10. Prove that tan alpha + 2tan 2alpha + 4tan 4alpha + 8cot 8alpha = cot ...

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  11. Find the sum: tan x + 1/2 tan x/2+ 1/2^(2) tan x/2^(2) +.....+1/2^(n-...

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  12. Prove that cosec 2alpha = cot alpha - cot 2alpha. Hence or otherwise ...

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  13. Prove that sum(r=1)^(10) = sin^(2) rpi/18 =5.

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  14. Sum the series: sin alpha - sin 2alpha + sin 3alpha - sin 4alpha + .....

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  15. Find sum(r=1)^(10) cos^(3) rpi/3.

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  16. Sum: sqrt(1 + sin 2alpha) + sqrt(1 + sin 4alpha) + sqrt(1 + sin 6alpha...

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  17. Prove that sin^(2) 12^circ + sin^(2)21^circ + sin^(2)39^circ + sin^(2)...

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  18. If A + B + C = pi, prove that cos A cosec B cosec C + cos B cosec C c...

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  19. Prove that in a triangle ABC, sin^(2)A - sin^(2)B + sin^(2)C = 2sin A...

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  20. Prove that in a triangle ABC, sum (cot B+ cotC)/(tan B + tan C) =1.

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