How to prove cosec4A + cot 4A = 1/2 (cotA-tanA)?

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Answer 1 · 2017-05-17T10:18:18

See the proof below

We need

#sin2A=2sinAcosA#

#Cos2A=cos^2A-sin^2A#

#cscA=1/sinA#

#cotA=cosA/sinA#

#tanA=sinA/cosA#

#LHS=csc4A+cot4A#

#=1/(sin4A)+(cos4A)/(sin4A)#

#=(1+cos4A)/(sin4A)#

#=(1+2cos^2(2A)-1)/(2sin2Acos2A)#

#=(2cos^2(2A))/(2sin2Acos2A)#

#=(cos2A)/(sin2A)#

#=(cos^2A-sin^2A)/(2sinAcosA)#

#=1/2(cosA/sinA-sinA/CosA)#

#=1/2(cotA-tanA)#

#=RHS#

#QED#