Let 2sin2x + 3 sin x – 2 > 0 and x2 – x – 2 < 0 (x is measured in radian). Then ‘x’ lies in the internal.
The number of points of intersection of the two curves y = 2 sin x and y = 5x2 + 2x + 3 is:
The number of all possible triplets (a1, a2, a3) such that
a1 + a2 cos 2x + a3 sin2x = 0 for all x is:
The equation sin4x – (k + 2) sin2x – (k + 3) = 0 possesses a solution if:
is where xo denotes the degrees:
If the mapping of f (x) = ax + b, a < 0 maps [–1, 1] onto [0, 2], then for all values of θ, A = cos2θ + sin4θ is: