Show that :
`r^n ( Cosntheta + iota Sinntheta ) = [ r ( Costheta + iota Sintheta ) ]^n`

Show that : Costheta /( 1 - Sintheta ) + Costheta /( 1 + Sintheta ) = 2/Costheta

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

Eliminate theta from costheta +sintheta = m "and" sectheta +cosectheta = n

If A=[[costheta,isintheta],[isintheta,costheta]], then prove by principal of mathematical induction that A^n=[[cosntheta, i sinn theta],[isin n theta, cos n theta]] for all nin NN.

If cosectheta-sintheta=m" and " sectheta-costheta=n , elimnate theta .

if theta_1, theta_2, theta_3, ........, theta_n are in AP then (sintheta_1 + sintheta_2 + ....... + sintheta_n) / (costheta_1 + costheta_2 + costheta_3 + ...... + costheta_n ) =?

If r sintheta=1,r costheta=sqrt(3) then the value of (r^(2)tantheta) is

Show that costheta.[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta.[{:(sintheta,-costheta),(costheta,sintheta):}]=I.

Show that every real orthogonal matrix is of any one of the forms {:[(costheta,-sintheta),(sintheta,costheta)]:}or{:[(costheta,sintheta),(sintheta,-costheta)]:}

((1+sintheta+i costheta)/(1+sintheta-i costheta))^n is equal to