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(1 / sec a – tan a )–( 1 / cos a )= (1/ cos a) –( 1/ sec a + tan a) prove it.

(1 / sec a – tan a )–( 1 / cos a )= (1/ cos a) –( 1/ sec a + tan a) prove it.

Grade:12

2 Answers

Kaustubh Nayyar
27 Points
6 years ago
LHS=1/seca-tana   –   1/cosa
       = cosa /(1- sina) – 1/cosa =  (cos2a – (1 – sina))/(1 – sina)(cosa)
        = (sina – sin2a)/(1 – sina)(cosa) = (sina)(1 – sina)/(1 – sina)(cosa)
       =  tana
RHS=1/cosa – 1/(seca+tana)  =  (1/cosa) –( cosa/(sina+1))
       =  (sina +1  – cos2a)/(cosa)(sina+1)  =  (sina +1 +sin2a – 1)/(sina+1)(cosa)
       = sina/cosa = tana
Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the solution to your problem.
 
LHS = 1/(seca-tana) – 1/cosa
       = cosa /(1 – sina) – 1/cosa
       =  (cos2a – (1 – sina))/(1 – sina)(cosa)
       = (sina – sin2a)/(1 – sina)(cosa)
       = (sina)(1 – sina)/(1 – sina)(cosa)
       =  tana
 
RHS = 1/cosa – 1/(seca+tana)  
        =  (1/cosa) – ( cosa/(sina+1))
        =  (sina +1  – cos2a)/(cosa)(sina+1)  
        =  (sina +1 +sin2a – 1)/(sina+1)(cosa)
        = sina/cosa
        = tana
 
Hence, LHS = RHS
Hence proved.
 
Thanks and regards,
Kushagra

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