If `tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha)` then show that ` sinalpha+cosalpha=sqrt(2)costheta`.

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

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

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

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

(sqrt2-sinalpha-cosalpha)/(sinalpha-cosalpha) is equal to (a) sec(alpha/2-pi/8) (b) cos(pi/8-alpha/2) (c) tan(alpha/2-pi/8) (d) cot(alpha/2-pi/2)

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1) , find alpha

If A=[(0,sin alpha, sinalpha sinbeta),(-sinalpha, 0, cosalpha cosbeta),(-sinalpha sinbeta, -cosalphacosbeta, 0)] then (A) |A| is independent of alpha and beta (B) A^-1 depends only on beta (C) A^-1 does not exist (D) none of these

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1) , find alpha .

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)

If (2sinalpha)/(1+cosalpha +sinalpha)=y , then prove that (1-cosalpha+sinalpha )/(1+sinalpha) is also equal to y.