Find the inverse of `[(1, 0, 0),( 0,cosalpha,sinalpha),(0,sinalpha,-cosalpha)]`

Find the inverse the matrix (if it exists)given in [(1, 0, 0),( 0,cosalpha ,sinalpha),(0, 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 the following: |[cosalpha, sinalpha],[sinalpha, cosalpha]|

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 intsinx/(sin(x-alpha))dx=Ax+Blogsin(x-alpha)+C , then value of (A,B) is (A) (-sinalpha,cosalpha) (B) (-cosalpha,sinalpha) (C) (sinalpha,cosalpha) (D) (cosalpha,sinalpha)

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

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

Givent that pi/2 lt alphaltpi then the expression sqrt((1-sinalpha)/(1+sinalpha))+sqrt((1+sinalpha)/(1-sinalpha)) (A) 1/(cosalpha) (B) - 2/(cosalpha) (C) 2/(cosalpha) (D) does not exist

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

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