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Prove that: "sin"(pi)/(5)"sin"(2pi)/(...

Prove that:
`"sin"(pi)/(5)"sin"(2pi)/(5)"sin"(3pi)/(5)"sin"(4pi)/(5)=(5)/(16)`
`"sin"36^(@) "sin"72^(@) "sin"108^(@) sin 144^(@)=(5)/(16)`.

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The correct Answer is:
`= (3)/(16)`
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LUCENT PUBLICATION-ADVANCED TRIGONOMETRIC IDENTITIES-EXERCISE 13A
  1. Prove that: "sin"(pi)/(5)"sin"(2pi)/(5)"sin"(3pi)/(5)"sin"(4pi)/(5)...

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  2. If p and q are two quantities such that p^(2) +q^(2) =1, then maximum...

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  3. If theta is real then 3 - cos theta + cos (theta + (pi)/(3)) lies in t...

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  4. If sinA=(1)/(sqrt(10))andsinB=(1)/(sqrt(5)), where A and B are positiv...

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  5. If cos (theta - alpha) = a, cos (theta - beta) = b, then the value of ...

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  6. A positive acute angle is divided into two parts whose tangents are 1/...

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  7. In trianglePQR, angleR = (pi)/(2). If tan((P)/(2)) " and " tan ((Q)/...

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  8. The value of (sin 55^(@) - cos 55^(@))/(sin10^(@) is

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  9. The value of cos 15^(@) - sin 15^(@) is

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  10. Minimum value of 27^(cos 2x) 81^( sin 2x) is

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  11. 3 (sinx - cosx)^(4) + 6 (sinx + cosx)^(2) + 4(sin^(6)x + cos^(6)x) =

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  12. If sin theta = sin 15^(@) + sin 45^(@), " where " 0^(@) lt theta lt ...

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  13. If cos alpha + cos beta = 0 = sin alpha + sin beta, then value of cos...

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  14. If A + B = 45^(@), " then " (cot A - 1) ( cot B - 1) is

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  15. If alpha, beta in (0, (pi)/(2)), sin alpha = (4)/(5) " and " cos (alp...

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  16. The value of tan 40^(@) + tan 20^(@) + sqrt(3) tan 20^(@) tan 40^(@) ...

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  17. The value of cos 20^(@) + Cos 100^(@) + cos 140^(@) is

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  18. If (-pi)/(2) < theta < (pi)/(2) " and " theta ne pm (pi)/(4), then th...

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  19. If sin theta =3 sin ( theta + 2 alpha), then the value of tan (theta...

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  20. If x=ycos""(2pi)/(3)=zcos""(4pi)/(3), then xy+yz+zx is equal to

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  21. (cos 9^(@) + sin 9^(@))/(cos 9^(@) - sin 9^(@)) equals

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