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If (1 + sin 2x)/(1- sin2x) = tan^(2) *(a...

If `(1 + sin 2x)/(1- sin2x) = tan^(2) *(alpha +x)` for all x then the numerically smallest value of `alpha` = ______.

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. The numerical value of tan 225^circ *cot 405^circ + tan 765^circ* cot...

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  2. The numerical value of cos 2pi/7 + cos 4pi/7 + cos 6pi/7 is=........

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  3. If (1 + sin 2x)/(1- sin2x) = tan^(2) *(alpha +x) for all x then the ...

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  4. If cos(x -y), cos x and cos(x + y) are in HP then cos x* sec (y/2)= .

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  5. If A, B, C are in AP and B = pi/4 , then tan A *tan B*tan C = .

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  6. If p in (0, pi) then the set of values of p for which sin p* cos^(3) ...

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  7. sec^(2)theta = 4xy/(x+y)^(2) is true if and only if

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  8. If cos theta + sec theta = 2 then cos^(n)theta+ sec^(n)theta is equal ...

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  9. If alpha = theta1 +theta2 and x = theta1 -theta2 and tan theta1 = lamb...

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  10. If ABCD is a cyclic quadrilateral then cos A + cos B + cos C + cos D ...

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  11. tan 40^circ + 2tan 10^circ is equal to

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  12. If cos(alpha + gamma)/cos(alpha - gamma) = cos 2beta then tan alpha, t...

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  13. The value of sqrt3 cosec 20^circ - sec 20^circ is equal to

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  14. The number of real values of x for which sin(e^x) = 5^(x)+5^(-x) is

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  15. If cot y= (sin x- sin z)/(cos z- cos x) then which of the following ...

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  16. The value of cos^(2)x + cos^(2) (pi/3 + x) - cos x *cos(pi/3+ x) is

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  17. The equation (cos p-1) x^(2) + cos p*x + sin p = 0 where x is a varia...

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  18. If tan ((pi)/(4) + theta) + tan ((pi )/(4) - theta) = p sec 2 theta) t...

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  19. The value of sin sqrt(x^(2) - pi^(2)/36) lies in the interval

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  20. If alpha, beta are two values lying between 0 and 2pi for which tan t...

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