202 The value of sin pi/n + sin 3pi/n + sin 5pi/n + - Maths - Trigonometric Functions

Question

202 The value of sin pi/n + sin 3pi/n + sin 5pi/n + to n terms is
equal to
i) 1
ii) 0
iii) n/2
iv n-1/2

Neha Sethi · Accepted Answer

sinπn+sin3πn+sin5πn+
sin2n-1πn=sinπn+sin2n-1πn+sin3πn+sin2n-3πn+
  sinπ=2sin2n-1πn+πn2cos2n-1πn-πn2+2sin2n-3πn+3πn2cos2n-3πn-3πn2+
sinπ=2sin2nπ2ncos2π-2πn2+2sin2nπ2ncos2π-6π2n2+
sinπ=2sinπcosπ-πn+2sinπcosπ-3π2n+
sinπ=0+0+0 +0=0Note:sinA+sinB=2sinA+B2cosA-B2sinπ=0

202. The value of sin pi/n + sin 3pi/n + sin 5pi/n + ...... to n terms is equal to i) 1 ii) 0 iii) n/2 iv n-1/2

202. The value of sin pi/n + sin 3pi/n + sin 5pi/n + ...... to n terms is equal to
i) 1
ii) 0
iii) n/2
iv n-1/2