If `A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1)` is equal to a.`A(-alpha,-beta)` b. `A(-alpha,beta)` c. `A(alpha,-beta)` d. `A(alpha,beta)`

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to

If cot(alpha+beta)=0, then sin(alpha+2 beta) is equal to

If F(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] and G(beta)=[(cosbeta, 0, sinbeta),(0, 1, 0),(-sinbeta, 0, cosbeta)], then [F(alpha)G(beta)]^-1 is equal to (A) F(-alpha)G(-beta) (B) G(-beta)F(-alpha0 (C) F(alpha^-1)G(beta^-1) (D) G(beta^-1)F(alpha^-1)

If cos alpha+cos beta=0=sin alpha+sin beta, then cos2 alpha+cos2 beta is equal to (a)-2sin(alpha+beta)(b)-2cos(alpha+beta)(c)2sin(alpha+beta)(d)2cos(alpha+beta)

If sinalpha+sin beta=a and cos alpha+cos beta=b,then sin(alpha+beta)=

Let F(alpha)=[{:(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1):}] and G(beta)=[{:(cosbeta,0,sinbeta),(0,1,0),(-sinbeta,0,cosbeta):}] . Show that [F(alpha).G(beta)]^(-1)=G(-beta).F(-alpha) .

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) where alpha,beta in[0,(pi)/(2)], then tan(alpha+2 beta)tan(2 alpha+beta) is equal to

If cos alpha+cos beta=0=sin alpha+sin beta, then cos2 alpha+cos2 beta is equal to

If cot(alpha+beta)=0, then sin(alpha+2 beta) can be (a)-sin alpha(b)sin beta(c)cos alpha(d)cos beta