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If sin alpha + cos alpha = lambda then f...

If `sin alpha + cos alpha = lambda` then find `|sin^(6) alpha - cos^(6) alpha|` in terms of `lambda`.

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. A factor of cos 4theta - cos 4phi is

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  2. The chord AB of a circle subtends an angle of frac {2pi}{3} at a point...

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  3. If sin alpha + cos alpha = lambda then find |sin^(6) alpha - cos^(6) a...

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  4. A container is filled with a simple of gas having molecules with speed...

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  5. AB and CD are two parallel chords of a circle of radius 6 cm lying on ...

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  6. Eliminate theta between cosec theta -sin theta = m and sec theta - cos...

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  7. If cos alpha + cos 2alpha = p,sin alpha + sin 2alpha = q then eliminat...

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  8. If cos alpha = cos beta*cos phi= cos gamma *cos theta and sin alpha = ...

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  9. Eliminate theta between a = cos(theta - alpha), b = sin(theta - beta) ...

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

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

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

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

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

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

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

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

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

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

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

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