Prove that :

sec 40° sin 50° + cos 40° cosec 50° = 2.

L.H.S. = sec 40° sin 50° + cos 40° cosec 50°

= sec (90° - 50°) sin 50° + cos (90° - 50°) cosec 50°

= cosec 50° sin 50° + sin 50° cosec 50°

= $\dfrac{1}{\text{sin 50°}}$ sin 50° + sin 50° $\dfrac{1}{\text{sin 50°}}$

= $\dfrac{1}{\cancel{sin 50°}} \cancel{sin 50°} + \cancel{sin 50°} \dfrac{1}{\cancel{sin 50°}}$

= 1 + 1

= 2

R.H.S. = 2

∴ L.H.S. = R.H.S.

Hence, sec 40° sin 50° + cos 40° cosec 50° = 2.