`sintheta+sqrt(3)costheta=6x-x^2-11 ,0lt=4thetapi,x in R ,` hold for no values of `xa n dtheta` `on ev a l u eof` x and two values of `theta` two values of `x` and two values of `theta` two point of values of `(x ,theta)`

If sintheta=sqrt(3)costheta,-pi

If sin theta =x, " write the value of " cot theta.

If sec theta =x, " write the value of " tan theta.

Find the values of p if it satisfy, cos theta = x + p/x, x in R for all real values of theta .

If sintheta+costheta=1 , then the value of sin2theta is

If 0 le theta lt pi/2 and costheta + sqrt(3) sin theta =2 , then what is the value of theta ?

If costheta =-1/2 and 0 lt theta lt 360^(@) , then the value of theta are

If hat u and hat v are unit vectors and theta is the acute angle between them, then 2 hat uxx3 hat v is a unit vector for (1) exactly two values of theta (2) more than two values of theta (3) no value of theta (4) exactly one value of theta

If the equation (lamda-1)x^2+(lamda+1)x+lamda-1=0 has real roots then lamda= (sintheta)/(costheta).(cos3theta)/(sin3theta) for (A) only one value of theta (B) for infinitely many values of theta (C) for no value of theta (D) of only two values of theta

Find maximum and minium value of 5costheta+3sintheta(theta+pi/6) for all real values of theta .