Question

prove that 1/sec A +tanA-1/cos A=1/cos A-1/sec A-tanA​

Answer 1

Answer:

LHS = 1/seca – tana – 1/cosa

= cosa /(1- sina) – 1/cosa = (cos^2a – (1 – sina))/(1 – sina)(cosa)

= (sina – sin^2a)/(1 – sina)(cosa)

= (sina)(1 – sina)/(1 – sina)(cosa)

= tana

RHS = 1/cosa – 1/(seca+tana) = (1/cosa) –(cosa/(sina+1))

= (sina +1 – cos^2a)/(cosa)(sina+1)

= (sina +1 +sin^2a – 1)/(sina+1)(cosa)

= sina/cosa

= tana