If `theta_(1), theta_(2), theta_(3), theta_(4)` are roots of the equation `"sin" (theta + alpha) =k "sin"2theta` no two of which differ by a multiple of `2pi`, then `theta_(1) + theta_(2) + theta_(3) + theta_(4)` is equal to

The solution of the equation 1-"cos" theta = "sin" theta "sin" (theta)/(2) is

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

If sin^(3) theta+sin theta cos theta+ cos^(3) theta=1 , then theta is equal to (n in Z)

The range of the function f (theta) =(sin theta)/( theta ) + (theta)/(tan theta) , theta in (0, (pi)/(2)) is equal to :

sin^(3)theta + sin theta - sin theta cos^(2)theta =

If tan theta_1,tantheta_2,tan theta_3,tan theta_4 are the roots of the equation x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0 then prove that tan(theta_1+theta_2+theta_3+theta_4)=cot beta

If tan theta_1,tantheta_2,tan theta_3,tan theta_4 are the roots of the equation x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0 then prove that tan(theta_1+theta_2+theta_3+theta_4)=cot beta

(1)/( sec 2 theta) = cos ^(4) theta - sin ^(4) theta.

For theta_(1), theta_(2), ...., theta_(n) in (0, pi/2) , if In (sec theta_(1)-tan theta_(1))+ "In" (sec theta_(2)-tan theta_(2))+...+"In" (sec theta_(n)-tan theta_(n))+ "ln" pi=0 , then the value of cos((sec theta_(1)+ tan theta_(1))(sec theta_(2)+tan theta_(2))....(sec theta_(n)+tan theta_(n))) is equal to

If 1/2 sin^(-1)((3sin2theta)/(5+4cos2theta))=(pi)/4 , then tan theta is equal to