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Prove that"sin"(pi)/(14)"sin"(3pi)/(14)"...

Prove that`"sin"(pi)/(14)"sin"(3pi)/(14)"sin"(5pi)/(14)"sin"(7pi)/(14)=(1)/(8)`

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If alpha = (2pi)/7 prove that tan alpha *tan 2alpha + tan 2alpha* tan ...

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  2. If alpha = 2pi/7 prove that sec alpha + sec 2alpha + sec 3alpha = -4.

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  3. Prove that"sin"(pi)/(14)"sin"(3pi)/(14)"sin"(5pi)/(14)"sin"(7pi)/(14)=...

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  4. Show that :sin pi/7 *sin 2pi/7* sin3pi/7 = sqrt7/8

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  5. If u = sec theta + tan theta then tan theta in terms of u is.

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  6. If sin x + cos x = m(ne pm 1) and sec x + cosec x = n then n in terms ...

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  7. If alpha gt 0 such that tan(x + alpha) = tan x for all x in R then the...

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  8. If theta = 5pi/9 the sign of the expression cos theta + sin theta is.

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  9. If 5cos 2t + 12sin 2t = lambda sin(2t -tan^(-1)mu) where lambda, mu ar...

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  10. If cos A = 3/4 then the value of 32sin( A/2)* sin (5A/2) is.

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  11. If 0 lt beta lt alpha lt gamma and cos(alpha + beta) = 4/5, sin(alpha...

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  12. If alpha = 2pi/7 prove that tan alpha *tan 2alpha + tan 2alpha* tan 4a...

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  13. Let sin^(3)x* sin 3x = sum(m=0)^(n) cm cos mx be an identity in x wher...

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  14. If (cos (alpha1- alpha2))/(cos (alpha1+ alpha2)) = (cos (alpha3+ alph...

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  15. If sin x + sin y = a, cos x - cos y = b then the value of tan ((y-x)/2...

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  16. Find the value of sin^(2)5^(@)+ sin^(2)10^(@)+ sin^(2)15^(@)+* * * +si...

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  17. The numerical value of cos 2pi/7 + cos 4pi/7 + cos 6pi/7 is=........

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  18. The numerical value of sin pi/18 * sin 5pi/18* sin 7pi/18 is.............

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  19. The numerical value of tan 20^circ* tan 40^circ* tan 80^circ =.

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  20. The numerical value of cos(( pi)/15)* cos ((2pi)/15)* cos ((4pi)/15) ...

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