If `5tanalpha=4` , show that `(5sinalpha-3cosalpha)/(5sinalpha+2cosalpha)=1/6`

If 0 lt alpha lt pi/2 then show that tanalpha+cotalphagtsinalpha+cosalpha

If secalpha=5/4 , verify that (tanalpha)/(1+tan^2alpha)=(sinalpha)/(secalpha)

Prove that (sinalpha)/(1+cosalpha)+(1+cosalpha)/(sin alpha)=2"cosec "alpha .

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 (2sinalpha)/(1+cosalpha +sinalpha)=y , then prove that (1-cosalpha+sinalpha )/(1+sinalpha) is also equal to y.

(sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

A square of side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle alpha(0ltalphaltpi/ 4) with the positive direction of x-axis. equation its diagonal not passing through origin is (a) y(cosalpha+sinalpha)+x(sinalpha-cosalpha)="a (b) y(cosalpha+sinalpha)+x(sinalpha+cosalpha)=a (c) y(cosalpha+sinalpha)+x(cosalpha-sinalpha)=a (d) y(cosalpha-sinalpha)-x(sinalpha-cosalpha)=a

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

Find the amplitude of sinalpha+i(1-cosalpha)