Solve `2cos^2theta+sinthetalt=2,` where `pi/2lt=thetalt=(3pi)/2dot`

Solve : 2 cos^(2)theta + sin theta le 2 , where pi/2 le theta le (3pi)/2.

costheta - sintheta = 1/sqrt(2) (-pi lt theta lt pi)

Solve : 5cos2theta+2cos^2(theta/2)+1=0,-pi lt theta lt pi

Solve : cottheta+"cot"(pi/4+theta)=2

sin 2theta = cos 3theta (0 lt theta lt pi)

If x= sum_(n=0)^(oo) cos ^(2n)theta , y = sum _(n=o) ^(oo) sin ^(2n)theta, z= sum _(n=0)^(oo) cos ^(2n)theta.sin ^(2n)theta and 0 lt theta lt (pi)/(2) then-

Solve: 2 cos theta+ 2sqrt2 = 3 sec theta

The sum of all the solutions of cottheta=sin2theta(theta!=npi, n integer) , 0lt=thetalt=pi, is

If alpha is a root of 25 cos^2 theta+5 cos theta-12=0, pi/2 lt alpha lt pi , then sin 2alpha=

Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and the unit vector vec c is inclined at an angle theta to both vec aa n d vec bdot If vec c=m vec a+n vec b+p( vec axx vec b),(m ,n , p in R), then a. -pi/4lt=thetalt=pi/4 b. pi/4lt=thetalt=(3pi)/4 c. 0lt=thetalt=pi/4 d. 0lt=thetalt=(3pi)/4