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Prove that sin 27^circ = 1/4 (sqrt(5 + s...

Prove that `sin 27^circ = 1/4 (sqrt(5 + sqrt5) - sqrt(3 - sqrt5))`.

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Prove that sin 9^circ = 1/4 (sqrt(3 + sqrt5) - sqrt(5 - sqrt5)) .

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Prove that (1)cos36^(@)cos72^(@)cos108^(@)cos144^(@)=(1)/(16)(2) Show that 4sin27^(@)=sqrt(5+sqrt(5))-sqrt(3-sqrt(5))

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that cot 142.5^circ = sqrt2 + sqrt3 - sqrt4 - sqrt6.

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  2. Prove that sin 23pi/24 = sqrt((2 sqrt2 - sqrt3 -1)/(4 sqrt2))

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  3. Prove that sin 27^circ = 1/4 (sqrt(5 + sqrt5) - sqrt(3 - sqrt5)).

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  4. Prove that sin 9^circ = 1/4 (sqrt(3 + sqrt5) - sqrt(5 - sqrt5)).

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  5. Prove that tan 20^circ* tan 80^circ = sqrt3 tan 50^circ.

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  6. Prove that (1+cos pi/9) (1 + cos 3pi/9) (1+ cos 5pi/9) (1 + cos 7pi/9...

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  7. Prove that sin 55^circ - sin 19^circ + sin 53^circ - sin 17^circ = co...

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  8. Prove that cos^(4)pi/8+cos^(4)(3pi)/(8)+cos^(4)(5pi)/8+cos^(4)(7pi)/...

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  9. Prove that tan 9^circ - tan 27^circ -tan 63^circ + tan 81^circ = 4.

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  10. Prove that cos^(4)pi/8+cos^(4)(3pi)/(8)+cos^(4)(5pi)/8+cos^(4)(7pi)/...

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  11. Prove that cos theta* cos 2theta* cos2^(2)theta * cos2^(3)theta x... ...

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

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

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

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

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

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

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

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

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

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