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paradox xyz cool Grade: 11
        

prove that:


i. cosec2A - cot2A = tanA


ii. 2sinAcos3A - 2sin3AcosA = sin4A/2

6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

1) 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


HENCE PROVED


 

6 years ago
vikas askiitian expert
510 Points
										

2)


   2SINACOS3A - 2SIN3ACOSA = SIN4A/2


 LHS =2SINACOSA(COS2A - SIN2A)


 COS2A - SIN2A =COS2A   &   2SINACOSA =SIN2A


 LHS =SIN2ACOS2A


        =(2SIN2ACOS2A)/2


        =SIN4A/2                                  (using sin2x = 2sinxcosx)


hence proved

6 years ago
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