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prove that: i. cosec2A - cot2A = tanA ii. 2sinAcos 3 A - 2sin 3 AcosA = sin4A/2

prove that:


i. cosec2A - cot2A = tanA


ii. 2sinAcos3A - 2sin3AcosA = sin4A/2

Grade:11

3 Answers

vikas askiitian expert
509 Points
10 years ago

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

 

vikas askiitian expert
509 Points
10 years ago

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

Saroj Koiry
23 Points
4 years ago
Cosec2A= cot2A+tanA=> RHS=cot2A+tanACos2A/sin2A+sinA/cosACos2A*cosA+sin2A*sinA/sin2A.cosaCos(2A-A)/sin2A.cosACosA/sin2A.cosA1/sin2A=cosec2A

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