Question

11th science trigonometry

find the value of eqation

Answer 1

Modification
2sin π/11.cos π/11+2sinπ/11.cos 3π/11+2sinπ/11.cos5π/11+2sinπ/11.cos7π/11+2sinπ/11.cos9π/11

using identity 2sin A Cos B=sin(A+B)+(sinA-B)

sin(π/11+π/11)+sin(π/11-π/11)+sin(π/11+3 π/11)+sin(π/11-3π/11)+sin(π/11+5π/11)+sin(π/11-5π/11)+sin(π/11+7π/11)+sin(π/11-7π/11)+sin(π/11+9π/11)+sin.(π/11-9π/11)
____________________________________
2sinπ/11

using sin(-a) =-sin(a)
sin (2π/11)+sin(0)+sin4π/11-sin2π/11+sin6π/11-sin4π/11+sin8π/11-sin6π/11+sin10π/11-sin8π/11

sin10π/11
_______
2sinπ/11
=sinπ/11
________
2sinπ/11
= 1/2
1/2+cos11π/11+cos13π/11
=-1/2-cos2π/11


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