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Show that the maximum and minimum values of `sqrt(a^(2)cos^(2)theta + b^(2)sin^(2) theta) + sqrt(a^(2)sin^(2)theta + b^(2)cos^(2)theta)` are `sqrt(2(a^(2) +b^(2))` and a + b respectively.

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A DAS GUPTA-Circular Functions, Identities -Exercise
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  2. Find the minimum value of 9tan^(2)theta + 4cot^(2)theta.

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

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

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  5. Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi...

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  6. Show that (sec^(2)theta - tan theta)/(sec^(2)+ tan theta) lies betwe...

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  7. Prove that tan alpha + 2tan 2alpha + 4tan 4alpha + 8cot 8alpha = cot ...

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  8. Find the sum: tan x + 1/2 tan (x/2)+ 1/2^(2) tan (x/2^(2)) +.....+1/2...

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  9. Prove that cosec 2theta = cot theta - cot 2theta . Hence or otherwi...

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  10. Prove that sum(r=1)^(9) sin^(2) rpi/18 =5.

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

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

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

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

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

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

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  17. If A + B + C + D = 2pi, prove that: cos A + cos B + cos C + cos D =...

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  18. If alpha + beta- gamma= pi, prove that sin^(2)alpha + sin^(2)beta - s...

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  19. If alpha + beta + gamma = 2 theta, prove that cos theta + cos(theta- ...

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  20. If A + B + C = pi, show that cot A + sinA/(sin B sin C) = cot B + sin...

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