IF `sintheta+costheta =3/2` then find `sintheta .costheta=?`

If 3sintheta+4costheta =5 then find the value of: 4sintheta-3costheta

If 3sintheta+5costheta=5, then show that 5sintheta-3costheta=+-3.

If 3sintheta+5costheta=5, then show that 5sintheta-3costheta=+-3.

If sintheta + 2 costheta=1 ,then prove that 2sintheta-costheta=2 .

Let P = [theta : sintheta – costheta = sqrt2 costheta) andQ= {theta : sintheta + costheta = 12 sintheta} be two sets. Then:

Eliminate theta in the following (i) 2sintheta=x, 3costheta=y (ii) costheta + sintheta=x, costheta-sintheta=y

If A=[[costheta -sintheta], [[sintheta , costheta]]] , then find the values of theta satisfying the equation A^T+A=I_2 .

If costheta+sintheta=sqrt(2)costheta ,then find the value of (costheta-sintheta)/(sintheta) .

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

If a costheta + b sintheta=3 and a sintheta - b costheta=4 , then a^(2)+b^(2) has the value 25