Number of roots of `cos^2x+(sqrt(3)+1)/2sinx-(sqrt(3))/4-1=0` which lie in the interval `[-pi,pi]` is 2 (b) 4 (c) 6 (d) 8

The number of roots of equation cos^(7)theta - sin^(4)theta = 1 that lie in the interval [0,2pi] is-

The number of solution(s) of the equation cos2theta=(sqrt(2)+1)(costheta-1/(sqrt(2))) , in the interval (-pi/4,(3pi)/4), is 4 (b) 1 (c) 2 (d) 3

The number of distinct real roots of |sinxcosxcosxcosxsinxcosxcosxcosxsinx|=0 in the interval -pi/4lt=xlt=pi/4 is 0 (b) 2 (c) 1 (d) 3

The number of distinct real roots of |sinxcosxcosxcosxsinxcosxcosxcosxsinx|=0 in the interval -pi/4lt=xlt=pi/4 is 0 (b) 2 (c) 1 (d) 3

Numbers of real roots of the equation (sqrt(5)-sqrt(3))cos ecx+(sqrt(5)+sqrt(3))sec x=8 in [0,4 pi]

The number of distinct roots of |(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx,cosx,sinx)|=0 in the interval -pi/4 le x le pi/4 is (A) 0 (B) 2 (C) 1 (4) 2

The number of solution of the equation |2sin x-sqrt(3)|^(2cos^(2)x-3cos x+1)=1 in [0,pi] is 2 (b) 3(c)4 (d) 5

The solution set of the equation 4s int h eta cos theta-2cos theta-2sqrt(3)s int_(h eta)+sqrt(3)=0 in the interval (0,2 pi) is {(3 pi)/(4),(7 pi)/(4)} (b) {(pi)/(3),(5 pi)/(3)}{(3 pi)/(4),pi,(pi)/(3)(5 pi)/(3)}(d){(pi)/(6),(5 pi)/(6),(11 pi)/(6)}

Number of critical points of the function. f(x)=(2)/(3)sqrt(x^(3))-(x)/(2)+int_(1)^(x)((1)/(2)+(1)/(2)cos2t-sqrt(t)) dt which lie in the interval [-2pi,2pi] is………. .

The number of solution of sqrt3Cos^2x=(sqrt3-1)Cosx+1 , x in [0,pi/2]