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If cos(x -y), cos x and cos(x + y) are i...

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

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. The numerical value of cos 2pi/7 + cos 4pi/7 + cos 6pi/7 is=........

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

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

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

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

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  6. sec^(2)theta = frac{4xy}{(x+y)^(2)} is true if and only if

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

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

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

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  10. tan 40^@ + 2tan 10^@ is equal to

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

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

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

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

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  15. What is the real part of ( sin x + icos x )^(3), where i= sqrt( -1) ?

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  16. If alpha, beta be the solutions of theta for the equation a tan theta...

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

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

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  19. If tan theta + tan (pi/3 +theta) + tan (frac{2pi}{3}+ theta) = k tan 3...

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

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