sin alpha+sin(alpha+beta)+sin(alpha+2 beta)+......+sin(alpha+bar(n-1)beta)=(sin(n beta)/(2))/(sin(beta)/(2))sin(alpha+(n-1)/(2)beta)

Statement-1: sin10^(@)+sin120^(@)+....+sin350^(@)=0 Statement-2: sin alpha+sin (alpha+beta)+....+sin(alpha+(n-1)beta)=(sin(alpha+((n-1)beta)/(2))sin((nbeta)/(2)))/(sin((beta)/(2))), beta ne 2npi.

sin ^ (2) alpha + sin ^ (2) (alpha-beta) -2sin alpha cos beta sin (alpha-beta) = sin ^ (2)

Assertion A: sin((pi)/(n))+(sin(3 pi))/(n)+(sin(5 pi))/(n)+.... to n terms +0 Reason (alpha+beta)+...... to n terms =sin alpha+sin(alpha+beta)+...... to terms=(sin(n(beta)/(2)))/(sin((beta)/(2)))*sin((2 alpha+(n-1)beta)/(2))

Prove that for all ninN Cosalpha+cos(alpha+beta)+cos(alpha+2beta)+ . . . +cos[alpha+(n-1)beta] = (cos[alpha+((n-1)/(2))beta]"sin"((nbeta)/(2)))/("sin"(beta)/(2))

Prove that for all ninN Cosalpha+cos(alpha+beta)+cos(alpha+2beta)+ . . . +cos[alpha+(n-1)beta] = (cos[alpha+((n-1)/(2))beta]"sin"((nbeta)/(2)))/("sin"(beta)/(2))

2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=

Assertion (A) : "sin" (pi)/(n)+"sin" (3pi)/(n)+"sin"(5pi)/(n)+....+ to n terms=0 Reason (R) : sin alpha+ sin (alpha+ beta)+...+ to n terms =(Sin ((n beta)/(2)))/(Sin beta//2)xxsin ((2 alpha+(n-1)beta)/(2))

Prove that: sin alpha+sin beta+sin gamma-sin(alpha+beta+gamma)=4sin((alpha+beta)/(2))sin((beta+gamma)/(2))sin((gamma+alpha)/(2))