[" ज्ञात कीजिए जिलके लिए "y=],[[0,(pi)/(2)]" में "y=(4sin theta)/((2+cos theta))-theta]

I=int_(0)^( pi/4)(sin2 theta)/(sin^(2)theta+cos^(4)theta)d theta

int_ (0) ^ ((pi) / (2)) (sin2 theta) / (sin ^ (4) theta + cos (4) theta) d theta

Evaluate int _(0)^(pi//2) (cos^(4) theta)/(sin^(4) theta + cos^(4) theta)d theta

int _(0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) theta )=

int _(0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) theta )=

If the system of linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

If the system of linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

Prove that y = (4 sin theta)/((2 + cos theta)) - theta is an increasing on theta in [0, (pi)/2] .