If `z= (cos theta, sin theta)`, find `(z-(1)/(z))`

Show that the solution of cos theta - sin theta = -1 is 2npi pm (3pi)/(4) - (pi)/(4), n in Z

S_(1) : If tan p theta = cot q theta " then " theta = ((2 n + 1) pi)/( p (P + q)), n in Z S_(2) : If tan (pi sin theta ) = cot (pi cos theta) , " then " sin (theta + (pi)/(4)) = pm (1)/(2 sqrt(2))

If (2 sin theta )/(1+ cos theta + sin theta )=x, find the value of (1- cos theta + sin theta )/(1+ sin theta )

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

Show that (1 + cos theta)/(sin theta)+ (sin theta)/(1 + cos theta) = 2 cosec theta .

If the matrix [(cos theta, sin theta, 0),(sin theta, cos theta, 0),(0,0,1)] is singular then theta=

If n is integer and z = cis theta, ( theta ne ( 2n + 1) pi//2) , then show that (z ^(2n) -1)/(z^(2n) +1) = i tan n theta .

I : If sin((pi)/(4)cot theta)=cos ((pi)/(4)tan theta) then theta = n pi+pi//4, n in Z II : If tan ((pi)/(2)sin theta)=cot((pi)/(2)cos theta) then sin (theta + (pi)/(4))= pm (1)/(sqrt(2))

The number of all possible values of theta where 0 lt theta lt pi for which the system of equations (y+z)cos 3 theta=(xyz)sin 3theta, x sin 3 theta=(2cos 3theta)/y+(2sin 3 theta)/y, (xyz) sin 3theta=(y+2z)cos 3 theta+y sin 3 theta has a solution (x_(0),y_(0),z_(0)) with y_(0)z_(0)!=0 is