Solve `tan(pi/2costheta)=cot(pi/2sintheta)`

IF tan ( pi cos theta) = cot ( pi sin theta ) then cos ( theta - (pi)/(4)) is equal to

Solve tan5theta=cot2theta

Evaluate int_(0)^(pi//2)(costheta)/((1+sintheta)(2+sintheta))d theta

Evaluate: int_(0)^(pi/2)(costheta)/((1+sintheta)(2+sintheta))d theta .

If n is positive integer prove that ((1+sintheta+icostheta)/(1+sintheta-icostheta))^(n)=cosn((pi)/(2)-theta)+isinn((pi)/(2)-theta) .

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

The value of the determinant |[sintheta, costheta, sin2theta] , [sin(theta+(2pi)/3), cos(theta+(2pi)/3), sin(2theta+(4pi)/3)] , [sin(theta-(2pi)/3), cos(theta-(2pi)/3), sin(2theta-(4pi)/3)|

Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tantheta/2

Prove that (sintheta-costheta+1)/(sintheta+costheta-1)=(1)/(sec theta-tan theta). using the identity sec^(2)theta=1+tan^(2)theta .

If costheta:sintheta=1:2 , then find the value of (8costheta-2sintheta)/(4costheta+2sintheta)