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In triangle ABC, B = pi/3 and sin A . si...

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

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If f(theta) = 11cos^(2)theta + 15sin theta cos theta - 9sin^(2)theta, ...

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

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

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

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

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

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

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

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

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

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  11. If tan^(3) (alpha/2+ pi/4) = tan(beta/2 +pi/4) then prove that sin be...

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

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

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  14. Prove that cos^(2)theta + cos^(2)(alpha + theta) – 2cos alpha *cos th...

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  15. If sin beta = 1/5 sin(2alpha +beta), show that tan(alpha +beta) = 3/2...

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  16. If Tn = sin^(n)theta + cos^(n)theta then prove that (T5 -T3): (T7- T5...

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  17. If f(alpha, beta) = cos^(4)alpha/cos^(2)beta + sin^(4)alpha/sin^(2)bet...

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  18. If cos A = tan B, cos B = tan C and cos C = tan A then show that sin A...

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  19. Prove that cos theta =(cos alpha- cos beta)/(1 -cos alpha*cos beta) ⇔ ...

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  20. If sqrt(a + b) tan( theta/2) = sqrt(a -b) tan (phi/2) then prove that ...

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