SOLUTION: Show that 2sin 4pi/5 cos pi/5 = sin 2pi/5

Question 1142055: Show that
2sin 4pi/5 cos pi/5 = sin 2pi/5
Answer by ikleyn(53756) (Show Source): You can put this solution on YOUR website!
.

First use the identity  


     = ,


which is valid for any angle .  From this identity, you get


     = .


It gives you


     = .


Next use the identity   = ,  which is valid for any angle  .  It gives you


     =  = .


It is what has to be proved.

RELATED QUESTIONS
If {{{sin^2 (pi/9)+sin^2 (2pi/9)+sin^2 (3pi/9)+sin^2(4pi/9)=9/4 }}}, evaluate {{{ cos^2... (answered by ikleyn)

cos theta=3/5, while 3pi/2 < theta < 2pi what is sin 2theta? I know that the equation is... (answered by Fombitz)

y=2sin(x-pi/2)find the amplitude, phas shift, and period for the graph of each function. (answered by lwsshak3)

Graph the function y=2sin(x-2pi/3). To draw the graph, plot all x-intercepts, minima and... (answered by stanbon)

please help me solve this: sin^2 2pi/5 - cos^2... (answered by solver91311)

Circle the Larger Number 1. a) tan^-1(-1/4) b) cos^-1(-1/4) 2. a)... (answered by jsmallt9)

Given: {{{cos(A)=-7/25}}}, {{{pi < A < 3pi/2}}} 
       {{{sin(B)=-3/5}}},... (answered by Edwin McCravy)
given that {{{cos(x) = 3/5}}}, {{{3pi/2 < x < 2pi}}} find 
{{{cos(x/2)}}},... (answered by Edwin McCravy)
Find all solutions for, 5 sin^2(x) plus sin(x)= cos^2(x), that lie between 0  =< x =<... (answered by lwsshak3)