If the lines `lambda x+(sin alpha)y+cosalpha=0, x+(cosalpha)y+sinalpha=0, x-(sinalpha)y+cosalpha=0` pass through the same point where `alpha in R` then `lambda` lies in the interval

If the lines lambda x+(sin alpha)y+cos alpha=0,x+cos alpha y+sin alpha=0,x-sin alpha y+cos alpha= pass through the point where alpha in R the lambda lies in the interval

The distance the points (sinalpha, cosalpha,0), (cosalpha, - sin alpha,0) is

Assertion : The system of linear equations x+(sinalpha)y+(cosalpha)z=0x+(cosalpha)y+(sinalpha)z=0x-(sinalpha)y-(cos\ alpha)z=0 has a non-trivial solution for only value of alpha lying the interval (0,\ pi) Reason: The equation in\ alpha cosalphas in alpha cosalphasinalpha cosalphasinalphac osalpha-sinalpha-cosalpha|=0 has only one solution lying in the interval (-pi/4,\ pi/4)

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

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

Let lamda and alpha real. Find the set of all values of lamda for which the system. x+(sinalpha)y+(cosalpha)z=0, x+(cosalpha)y+(sinalpha)z=0, -x+(sinalpha)y+(cosalpha)z=0 has a non trivial solution. For lamda=1 find all values of alpa.

If (2sinalpha)/(1+cosalpha+sinalpha) =x, then (1-cosalpha+sinalpha)/(1+sinalpha) =

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

If F(alpha)=[[cosalpha, -sinalpha, 0], [sinalpha, cosalpha, 0], [0, 0, 1]] , where alphainR , then (F(alpha))^(-1)=