Question

Prove that:

sin 48° sec 48° + cos 48° cosec 42° = 2

Answer 1

Taking L.H.S = sin 48° sec 48° + cos 48° cosec 42° 

= sin 48° sec (90° − 48°) cos 48° cosec (90° − 48°) [∵sec (90 – θ) = cosec θ and cosec (90 – θ) = sec θ] 

= sin 48°cosec 48° + cos 48°sec 48°  [∵ cosec θ x sin θ = 1 and cos θ x sec θ = 1] 

= 1 + 1

= 2

Hence proved