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 sec(theta+alpha)+sec(theta-alpha)=2\ s e ctheta, prove that costheta=+-sqrt(2)cosalpha/2dot

If tan^2 theta = 1+2 tan^2 phi , prove that cos 2 phi = 1 + 2 cos 2 theta .

If x sin alpha = y cos alpha, prove that : x/(sec 2alpha) + y/(cosec 2 alpha) = x

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 (alpha - 2 beta), sec alpha , sec (alpha + 2 beta) are in arithmetical progressin then cos ^(2) alpha = lamda cos ^(2) beta (beta ne n pi, n in I) the value of lamda is:

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

If cos theta = ( cos phi -e)/( 1- e cos phi ) , show that tan ""(theta)/( 2) = +- sqrt((1+e)/( 1-e)) tan ""(phi)/(2)

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

(cos alpha + 2 cos 3 alpha + cos 5 alpha )/(cos 3 alpha + 2 cos 5 alpha + cos 7 alpha ) = cos 3 alpha sec 5 alpha .

If cos(theta - alpha) , costheta , cos(theta + alpha) are in H.P. then costheta.sec(alpha)/2 =