Evaluate the following: ` |[tanalpha, cosecalpha],[sinalpha, cotalpha]| `

Evaluate the following: |[cosalpha, sinalpha],[sinalpha, cosalpha]|

Find the adjoint of the following matrices: [(cosalpha,sinalpha),(sinalpha,cosalpha)] (ii) [(1,tanalpha//2),(-tanalpha//2, 1)] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.

Evaluate: =|[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha,-sinbeta,0]|

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

If tanalpha+cotalpha=2 , then

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

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

If A=[[cosalpha, sinalpha],[-sinalpha, cosalpha]] , prove by mathematicasl induction that, A^n=[[cosnalpha, sin nalpha],[-sin nalpha,cos nalpha]] for every natural number n

If A=[ [0,-tan((alpha)/2)],[tan(alpha/2),0]] then (I-A)[[cosalpha,-sinalpha],[sinalpha,cosalpha]] =

Show without expanding at any stage that: [0,sinalpha-cosalpha],[-sinalpha,0,sinbeta],[cosalphas-sinbeta,0]|=0