Evaluate:sec 50° sin 40° + cos 40° cosec 50°

1.	Evaluate:sec 50° sin 40° + cos 40° cosec 50°
Answer» We know that, sin (90 – θ) = cos θ and cos (90 – θ) = sin θ So, the given can be expressed as sec 50° sin (90 – 50)° + cos (90 – 50)° cosec 50° = sec 50° cos 50° + sin 50° cosec 50° = 1 + 1 [∵ sin θ x cosec θ = 1 and cos θ x sec θ = 1] = 2

Answer»

We know that,

sin (90 – θ) = cos θ and cos (90 – θ) = sin θ

So, the given can be expressed as

sec 50° sin (90 – 50)° + cos (90 – 50)° cosec 50°

= sec 50° cos 50° + sin 50° cosec 50°

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

= 2

Discussion