[" 1."cos(n+1)alpha*cos(n-1)alpha+sin(n+1)alpha*sin(n-1)alpha=],[" 1) "cos2n alpha," 3) "sin2n alpha]quad " as "2 alpha

( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha + cos (n-1) alpha )=

if cos^(2)alpha-sin alpha=(1)/(n) then alpha

1/(cos alpha + cos 3 alpha)+ 1/(cos alpha + cos 5 alpha)+ 1/(cos alpha + cos 7 alpha) +....+ 1/(cos alpha +cos(2n+1) alpha) = 1/2 "cosec" alpha[tan (n+1) alpha - tan alpha ]

If A=[cos alpha+sin alpha sqrt(2)sin alpha-sqrt(2)sin alpha cos alpha-sin alpha], prove that =[cos n alpha+sin n alpha sqrt(2)sin n alpha-sqrt(2)sin n alpha cos n alpha-sin n alpha] for all n in N.

If n-1,2,3,dot,t h e ncosalpha"cos"2alpha"cos"4alphacos2^(n-1)alphai se q u a lto (sin2nalpha)/(2nsinalpha) (b) (sin2^nalpha)/(2^n"sin"2^("n"-1)alpha) (c) (sin4^(n-1)alpha)/(4^(n-1)sinalpha) (d) (sin2^nalpha)/(2^n"sin"alpha)

If (2sinalpha)/({1+cos alpha+sin alpha})=y, then ({1-cos alpha+sin alpha})/(1+sin alpha)=

If y = (2 sin alpha )/(1 + cos alpha + sin alpha) then, prove that (1 - cos alpha + sin alpha)/(1 + sin alpha) = y .