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# prove that:i. cosec2A - cot2A = tanAii. 2sinAcos3A - 2sin3AcosA = sin4A/2

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

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