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Prove that in a triangle ABC, sinA/2 * s...

Prove that in a `triangle ABC`, `sinA/2 * sin B/2 *sin C/2 le 1/8` Also prove that equality holds if the triangle is equilateral.

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A DAS GUPTA-Trigonometrical Inequalities and Inequations -Exercise
  1. Prove that in a triangle ABC, sinA/2 * sin B/2 *sin C/2 le 1/8 Also p...

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  2. Prove that in a triangle ABC, sinA/2 * sin B/2 *sin C/2 le 1/8 Also p...

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  3. Prove that in triangle ABC, cos^(2)A + cos^(2)B + cos^(2)C lt 3/4.

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  4. Prove that if cot A + cot B + cot C = sqrt3, the triangle will be equ...

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  5. Prove that in an acute angled triangle ABC, tan A+tan B+ tan C ge 3sq...

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  6. Show that the greatest value of sin 2A + sin 2B +sin 2C in a triangle...

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  7. If A sube B and C sube D, then prove that: A xx C sube B xx D

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  8. Prove that sin^(2n)theta + cos^(2n)theta le 1 for all theta and n ge 1...

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  9. Find the set of all x in [0, pi] for which 2sin^(2)x - 3sin x + 1 ge ...

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  10. solve sin^(-1) x le cos^(-1) x

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  11. Solve: sin 2x gt cos x.

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  12. Solve: cos x + cos 2x + cos 3x = 0, x in [0, pi].

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  13. Solve: cos 3x + sqrt3 sin 3x + sqrt2 lt 0.

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  14. Solve: tan x = 3cot x.

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  15. In the following incomplete sentences, fill in the blanks so that the ...

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  16. In the following incomplete sentences, fill in the blanks so that the ...

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  17. In the following incomplete sentences, fill in the blanks so that the ...

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  18. If in a triangle ABC, the angle C is obtuse then tan A *tan B is

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  19. Prove that in a triangle ABC, sin^(2)A - sin^(2)B + sin^(2)C = 2sin A...

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