Cos65- cos5\ sin145=?

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Answer 1 · 2018-04-12T12:45:35

#-1#

We know that,

#color(red)((1)cosC-cosD=-2sin((C+D)/2)sin((C-D)/2)#

#color(blue)((2)sin(180-theta)=sin(pi-theta)=sintheta#

Here,

#(cos65-cos5)/sin145=color(red)((-2sin((65+5)/2)sin((65-5)/2)))/color(blue)(sin(180-35)#

#=(-2sin35sin30)/sin35#

#=-2sin30#

#=-2(1/2)#

#=-1#