If `cosalpha+secalpha=2`, show that `cos^3alpha+sec^3alpha=2`.

If 3cos alpha-4sinalpha=5 , show that, 3sinalpha+4cosalpha=0 .

sin alpha-cos alpha=m, show that : sin^(3)alpha-cos^(3)alpha=(3m-m^(3))/(2).

If cos^2alpha=sin^3alpha then show that tan^6alpha-tan^2alpha=1

if tan theta=(sinalpha-cosalpha)/(sinalpha+cosalpha) show that, sin alpha+cosalpha=pmsqrt(2)cos theta

If cotalphacotbeta=3 ,show that (cos(alpha-beta))/(cos(alpha+beta))=2

(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 secalpha+secbeta+secgamma=0 ,show that (cosalpha+cosbeta+cosgamma)^2=cos^2alpha+cos^2beta+cos^2gamma

If A= [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] ,show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 ,show that cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0