Trignometry - Prove Identity

1

cosec(Î /7)=cosec(2Î /7)+cosec(3Î /7)
therefore this is in the form...coseca= cosec2a + cosec3a........
but will this help?

62

yes this is the first step :)

1

1/sin(pi/7)=1/sin(2pi/7)+1/sin(3pi/7)

sin(2pi/7)*sin(3pi/7)/sin(pi/7)=sin(2pi/7)+sin(3pi/7)

2sin(pi/7)*cos(pi/7)*sin(3pi/7)/sin(pi/7)=sin(2pi/7)+sin(3pi/7)

2cos(pi/7)*sin(3pi/7)=sin(2pi/7)+sin(4pi/7)
[as sin(x)=sin(pi-x)]

now the above result is clearly true from sum to product formulas
i.e.
sin(x)+sin(y)=2sin(x+y/2)*cos(x-y/2)

hence proved

i guess this question is pretty damn simple

i want a harder one

Prove Identity