CosecA -2cot2AcosA=?

1 Answer
Dean R.
Jul 7, 2018

#csc A - 2 cot 2A cos A = 2 sin A#

Explanation:

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I'll assume that's #cot 2A# not #cot^2 A#

#csc A - 2 cot 2A cos A#

#= 1/sin A - {2 \cos 2A \cos A}/{sin 2A} #

#= 1/sin A - {2 \cos 2A \cos A}/{2 sin A cos A}#

#= 1/{sin A} - { \cos 2A }/{2 sin A }#

#= (1 - cos 2A)/{sin A} #

#={ (sin ^2 A + cos ^2A) - (cos^2 A - sin ^2 A)}/{sin A} #

#={ 2sin ^2 A }/{sin A} #

#= 2sin A #

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