证明csc4A + csc8A = cot2A-cot8A?

证明csc4A + csc8A = cot2A-cot8A?
Anonim

#RHS = cot2A-cot8A#

#=(cos2A)/(sin2A) - (cos8A)/(sin8A)#

#=(cos2Asin8A-cos8Asin2A)/(sin2Asin8A)#

#= SIN(8A-2A)/(sin2Asin8A)#

#=(2cos2Asin6A)/(2cos2Asin2Asin8A)#

#=(sin8A + sin4A)/(sin4Asin8A)#

#=(sin8A)/(sin4Asin8A)+(sin4A)/(sin4Asin8A)#

#= 1 /(sin4A)+ 1 /(sin8A)#

#= csc4A + csc8A = LHS#