If `costheta=tan^2((theta)/2)`show that `costheta=sqrt2-1`

If sintheta -cos theta=sqrt(2)costheta,"show that" sintheta+costheta=sqrt(2)sintheta(0ltthetalt pi/2).

If costheta+sintheta=sqrt2costheta , Prove that costheta-sintheta=sqrt2sintheta

If costheta= x/sqrt(x^2+y^2) show that x sin theta = y cos theta .

IF 2 costheta=x+1/x then show that 2 cos3 theta=x^3+1/x^3

If sin(pi costheta) = cos(pi sintheta) , show that, +- cos(theta +-pi/4) = (4n+-1)/(2sqrt(2)) , where n= any integer.

If cos theta -sin theta =sqrt(2) sin theta , show that, costheta+sintheta=sqrt(2) cos theta [0ltthetaltpi/2] .

Prove that all lines represented by the equation (2costheta+3sintheta)x+(3costheta-5sintheta)y=5costheta-2sintheta …(1) pass through a fixed point and its reflection in the line x+y=sqrt2 ? Prove that all lines through reflection point can be represented by the equation (2costheta+3sintheta)x+(3costheta-5sintheta)y= (sqrt2-1)(5costheta-2sintheta) ....(2)

4costheta cos 2theta cos3theta - 2cos 4theta=1

If P={theta:sintheta-costheta=sqrt2costheta} and Q={theta: sintheta+costheta=sqrt2 sintheta} , then show that P = Q.

int_(0)^((pi)/(2))(cos^(2)thetad theta)/(sintheta+costheta)=(1)/(sqrt(2))log(sqrt(2)+1)