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Prove that 2^(sin x) + 2^(cos x) ge 2^(1...

Prove that `2^(sin x) + 2^(cos x) ge 2^(1-1/sqrt2)` for all real x.

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that 2^(sin x) + 2^(cos x) ge 2^(1-1/sqrt2) for all real x.

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

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

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

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

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

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

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

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

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

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

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  12. If f(theta) = 11cos^(2)theta + 15sin theta cos theta - 9sin^(2)theta, ...

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

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  14. In triangle ABC, B = pi/3 and sin A . sin C = x then find the set of ...

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

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

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

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

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

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

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

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