Sin^8(75°)-cos^8(75°) ?

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Answer 1 · 2017-10-21T03:10:31

#Sin^8(75°)-cos^8(75°)#

#(Sin^4(75°)-cos^4(75°))(Sin^4(75°)+cos^4(75°)#

#=(Sin^2(75°)+cos^2(75°)) (Sin^2(75°)-cos^2(75°))(Sin^4(75°)+cos^4(75°)#

#=1*(- cos(2*75°))((Sin^2(75°)+cos^2(75°))^2-2sin^2 75* cos^2 75)#
#=(- cos(180-30))(1-1/2(2sin75* cos 75)^2)#

#=(cos(30))(1-1/2sin^2(150))#

#=sqrt3/2(1-1/2sin^2(180-30))#

#=sqrt3/2(1-1/2sin^2(30))#

#=sqrt3/2(1-1/8)#

#=(7sqrt3)/16#