If `sinalpha+cosalpha=sqrt2 cosalpha` then show that `tan2alpha=1`

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) , then show that sinalpha+cosalpha=sqrt(2)costheta .

If tanbeta=(n^2sinalpha cdot cosalpha)/(1-n^2sin^2alpha) then show that tan(alpha-beta)/(tanalpha)=1-n^2

If tantheta = (sinalpha-cosalpha)/(sinalpha+cosalpha), then (A) sin alpha-cos alpha=+-sqrt(2) sin theta (B) sinalpha+cosalpha=+-sqrt(2) cos theta (C) cos2theta=sin2alpha (D) sin2theta+cos2alpha=0

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

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

If A = {:((cosalpha, -sinalpha),(sinalpha, cosalpha):}) , then for what value of alpha is A an identity matrix?

if A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] be such that A+A'=I then alpha