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)`

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

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

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

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 0ltalphalt pi/4 equation (x-sinalpha)(x-cosalpha)-2=0 has (A) both roots in (sinalpha, cosalpha) (B) both roots in (cosalpha, sinalpha) (C) one root in (-oo, cosalpha) and other in (sinalpha, oo) (D) one root in (-oo,sinalpha) and other in (cosalpha, oo)

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

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

If A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]] , verify that A^T A=I_2

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

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