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

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
one year ago
Dear student,

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