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If A gt 0, B gt 0 and A + B = pi/3 then ...

If `A gt 0`, `B gt 0` and `A + B = pi/3` then find the maximum value of `tan A *tan B`.

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A DAS GUPTA-Circular Functions, Identities -Exercise
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  2. Prove that sin pi/14* sin 3pi/14* sin 5pi/14........... to 7 factors ...

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  3. If A gt 0, B gt 0 and A + B = pi/3 then find the maximum value of tan...

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  4. Find the minimum value of 9tan^(2)theta + 4cot^(2)theta.

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  5. Show that the maximum and minimum values of sqrt(a^(2)cos^(2)theta + ...

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  6. Find the set of possible values of (tan(x + pi/6))/tan x where x is an...

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  11. Prove that cosec 2alpha = cot alpha - cot 2alpha. Hence or otherwise ...

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  12. Prove that sum(r=1)^(10) = sin^(2) rpi/18 =5.

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  13. Sum the series: sin alpha - sin 2alpha + sin 3alpha - sin 4alpha + .....

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  14. Find sum(r=1)^(10) cos^(3) rpi/3.

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  15. Sum: sqrt(1 + sin 2alpha) + sqrt(1 + sin 4alpha) + sqrt(1 + sin 6alpha...

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  16. Prove that sin^(2) 12^circ + sin^(2)21^circ + sin^(2)39^circ + sin^(2)...

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  17. If A + B + C = pi, prove that cos A cosec B cosec C + cos B cosec C c...

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

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  19. Prove that in a triangle ABC, sum (cot B+ cotC)/(tan B + tan C) =1.

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  20. If A +B+C = 180^circ, prove that cos A/2+ cos B/2 +cos C/2 = 4cos (p...

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