if `costheta+sintheta=sqrt2 costheta,`prove that `costheta-sintheta=sqrt2sintheta`

lf costheta-sintheta=sqrt2sintheta prove that costheta+sintheta=sqrt2costheta .

If sintheta +costheta =sqrt(2) costheta then prove that costheta -sintheta=sqrt(2) sintheta

If a costheta -b sin theta = c ,then prove that a sintheta + b costheta=+-sqrt(a^2+b^2-c^2 )

If sin^2theta + sin^ 4theta = 1 , then prove that cos^2theta+ costheta= 1

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

If 3 tantheta+ cottheta = 5cosec theta, then prove that costheta =1/2

Prove that sintheta/(1+costheta) + (1+costheta)/sintheta = 2cosectheta

Evaluate : costheta[(costheta, sintheta),(-sintheta, costheta)]+sintheta[(sintheta,-costheta),(costheta, sintheta)]

If a costheta-b sintheta=c ,show that a sintheta+bcostheta=+-sqrt(a^2+b^2-c^2)

Solve: 2cos^2theta-3costheta+1=0