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If cos rx + cos ry = ar, r = 1, 2, 3 the...

If `cos rx + cos ry = a_r`, r = 1, 2, 3 then prove that `2a_1^(3) + a_3 = 3a_1(a_2 + 1)`.

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Eliminate theta between a = cos(theta - alpha), b = sin(theta - beta) ...

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  2. Eliminating alpha from xcos alpha = y cos(alpha +2pi/3) = zcos (alpha ...

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  3. If cos rx + cos ry = ar, r = 1, 2, 3 then prove that 2a1^(3) + a3 = 3...

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  4. Eliminate theta, phi from sin theta + sin phi = a, cos theta+ cos phi ...

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  5. Eliminatetheta from lambda cos 2theta = cos(theta + alpha) and lambda...

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  6. If f(theta) = 1 + sin [pi/4 + theta] + cos (pi/4 + theta). find the ra...

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  7. Prove that the value of 5 cos theta + 3cos (theta + pi/3) +3 lies bet...

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  8. Find the maximum and minimum values of sin^(6)x + cos^(6)x.

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  9. In triangle ABC, B = pi/3 and sin A : sin c = x then find the set of ...

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  10. Prove that the relation sin^(2)theta = (x+y)^(2)/4xy is not 4xy possi...

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  11. Prove that sin theta = x + p/x is possible for real x if p le 1/4

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  12. Show that there is no real x for which e^(sin x) - e^(-sin x) = 4.

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  13. If f(x) = 3(sin x - cos x)^(4) + 6(sin x + cos x)^(2) +4(sin^(6)x + co...

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  14. Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x *cos 2x *cos 3x.

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  15. If alpha, beta are acute angles and cos 2alpha = (3cos2beta -1)/(3-cos...

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  16. If tan theta* tan phi = sqrt((x-y)/(x+y)) prove that (x - y cos 2the...

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  17. If x in (pi, 2pi), prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(...

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  18. Show that cot theta* cot 2theta+ cot 2theta *cot 3theta + 2 = cot thet...

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  19. Prove that sin x* sin y*sin(x - y) + sin y *sin z*sin(y- z) + sin z ...

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  20. Prove that (3 + cos 4theta) cos 2theta = 4(cos^(8)theta - sin^(8)theta...

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