Prove the following i. cosec2A - cot2A = tanA ii. 2sinAcos^3A - 2sin^3AcosA = sin4A/2

i) cosec2a – cot2a = tana

lhs= 1/sin2a – cos2a/sin2a

=1-cos2a/sin2a

cos2a = 1-2sin2a &

sin2a =2sinacosa ,

by using these

lhs= [1- (1-2sin2a)]/2sinacosa

=2sin2a/2sinacosa=sina/cosa

=tana = rhs

ii) 2sinacos3a – 2sin3acosa = sin4a/2

lhs =2sinacosa(cos2a – sin2a)

cos2a – sin2a =cos2a &

2sinacosa =sin2a

lhs =sin2acos2a

=(2sin2acos2a)/2

=sin4a/2 (using sin2x = 2sinxcosx)

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