pranav ubarhande
Last Activity: 6 Years ago
Sin 11 will be equal to cos 79.now the whole expression will be cos 43+cos 29 - cos 79-cos65.now use formula
"cos c-cos d = 2 sin (c+d)/2 into sin ( d- c)/2" on 1st and 4th term and then on 2nd and 3rd term.
Now this whole expression will be converted into
2×sin108/2 ×sin 22/2 +2× sin 108/2×sin 50/2
Taking sin 54 common,
2sin54(sin11+ sin25).
Now again use formula for bracket ,
"Sin c+sin d =2sin (c+d)/2 into cos(c-d)/2"
Now the expression will be converted into
2sin 54(2sin 18 cos(-7))=2sin54(2sin18 cos7)as cos -x= cos
=4×sin54 sin 18 cos 7
Sin 54=(root5+1)/4, sin 18=(root5-1)/4 put values
Hence =cos7=sin 83 as "cos a=sin 90- a" hence proved sir
