Prove that for a null set `phi, n{P(P(phi))}=2`.

Prove that : P(n,n)= 2P (n,n -2)

Power set of the set A = {phi, {phi}} is

Find Power set of the set A={phi,{phi}} .

Prove that cos 2 theta cos 2 phi + sin ^(2) ( theta - phi) -sin ^(2) (theta + phi) = cos ( 2 theta + 2 phi).

If sin theta is G.M. of sin phi and cos phi, then prove that cos 2 theta = 2 cos ^(2) ((pi)/(4) + phi).

If sec(phi+alpha) + sec (phi-alpha) = 2 sec phi , prove that cos phi = pm sqrt(2) "cos"(alpha)/(2) , ( phi ne (pi)/(2)) .

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+phi)=cos (theta-phi) .

Prove the following: P(n , n)=2P(n , n-2)

The maximum number of equivalence relations on the set A = {phi , {phi}, {{phi}}} are

Prove that: ("sin"(x+theta))/("sin"(x+phi))=cos(theta-phi)+cot(x+phi)sin(theta-phi)dot