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

If 3cos alpha-4sinalpha=5 , show that, 3sinalpha+4cosalpha=0 .

If 0^(@)ltalphalt90^(@) , then solve the equation (sinalpha)/(1-cosalpha)+(sinalpha)/(1+cosalpha)=4 .

If A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] , then

If sinalpha+cosalpha=(1)/(5), find tan((alpha)/(2)).

If cotalpha=(15)/(8) , then ((2+2sinalpha)(1-sinalpha))/((1+cosalpha)(2-2cosalpha))=?

Without expanding show that |(0,sinalpha, -cosalpha),(-sinalpha,0,sinbeta),(cosalpha, -sinbeta,0)| = 0

If A={:[(0,-tan.alpha/2),(tan.alpha/2,0)]:} and I is the identify matrix of order 2, Show that I+A=(I-A) {:[(cosalpha,-sinalpha),(sinalpha,cosalpha)]:} .

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) , then sinalpha+cosalpha and sinalpha-cosalpha is equal to

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) , then sinalpha+cosalphaandsinalpha-cosalpha are equal to