Find real values of x for which, 27cos 2x . 81sin 2x is minimum. Also find this minimum value. [REE 2000, 3]
Solve the following system of equation for x and y and . [REE 2001 (mains), 3]
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The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution is [JEE 2002 (Screening), 3]
cos(a – b) = 1 and cos(a + b) = 1/e, where a, b Î [–p, p], number of pairs of a, b which satisfy both the equations is [JEE 2005 (Screening)]
If 0 < q < 2p, then the intervals of values of q for which 2 sin2q – 5sinq + 2 > 0, is [JEE 2006, 3]
The number of solutions of the pair of equations 2sin2q – cos 2q = 0 and 2cos2 q – 3 sin q = 0 in the interval [0, 2p] is [JEE 2007, 3]
For 0 < q < p/2, then solution(s) of (q + (m –1)p/4) cosec(q + mp/4) = 4 is(are) [JEE 2009]
The number of values of q in the interval such that for n=0, ±1, ±2 and tanq = cot 5q as well as sin2q = cos4q is [JEE 2010]
The number of all possible values of q when qÎ(0, p) for which the system of equation [JEE 2010]
(y + z) cos 3q = (xyz) sin 3q
x sin3q = (xyz) sin 3q = (y + 2z)cos 3q + y sin 3q have a solution (x0, y0, z0) with y0,z0 ¹ 0 is
Let P = {q : sin q – cos q = cos q} and Q = {q : sin q + cos q = sin q} be two sets. Then [JEE 2011]