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If alpha = 2pi/7 prove that tan alpha *t...

If `alpha = 2pi/7` prove that `tan alpha *tan 2alpha + tan 2alpha* tan 4alpha + tan 4alpha* tan a = - 7`

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If cos A = 3/4 then the value of 32sin( A/2)* sin (5A/2) is.

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

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

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

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

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

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

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

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

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

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

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  12. The numerical value of sin 6^circ* sin 42^circ* sin 66^circ* sin 78^c...

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  13. The numerical value of cot^(2)36^circ* cot^(2)72^circ =.

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  14. The numerical value of sin 12^circ* sin 48^circ* sin 54^circ= .

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  15. If sin 54^circ = 1/2 + sin theta, 0 lt theta lt pi/2, then theta = .

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  16. The numerical value of tan 225^circ *cot 405^circ + tan 765^circ* cot...

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

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  18. If (1 + sin 2x)/(1- sin2x) = tan^(2) *(alpha +x) for all x then the ...

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  19. If cos(x -y), cos x and cos(x + y) are in HP then cos x* sec (y/2)= .

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  20. If A, B, C are in AP and B = pi/4 , then tan A *tan B*tan C = .

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