If `t a ntheta=(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 .

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

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

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

Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

(sqrt2-sinalpha-cosalpha)/(sinalpha-cosalpha) is equal to (a) sec(alpha/2-pi/8) (b) cos(pi/8-alpha/2) (c) tan(alpha/2-pi/8) (d) cot(alpha/2-pi/2)

If A=[(0,sin alpha, sinalpha sinbeta),(-sinalpha, 0, cosalpha cosbeta),(-sinalpha sinbeta, -cosalphacosbeta, 0)] then (A) |A| is independent of alpha and beta (B) A^-1 depends only on beta (C) A^-1 does not exist (D) none of these

If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] is identity matrix, then write the value of alpha .

Let A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] , then :