Question

Evaluate sin (50° + θ) – cos (40° – θ) + tan 1° tan 15° tan 20° tan 70° tan 65° tan 89°+ sec (90°– θ). cosec θ – tan (90° – θ) cot θ.

(a) 0

(b) 1

(c) 2

(d) 3

Answer 1

Correct option is (c) 2

sin(50° + θ) − cos(40° − θ) + tan 1° tan 15° tan 20° tan 70° tan 75° tan 89° + sec(90° − θ).cosec − tan(90° − θ)cot θ =

cos(90° − (50° + θ)) − cos(40° − θ) + cot(90° − 15°).cot(90° − 20°)tan 75° tan 89° + cosec θ.cosec θ − cot θ.cot θ

= cos(40° − θ) − cos(40° − θ) + cot 89° cot 75° cot 70° tan 70° tan 75° tan 89° + cosec²θ − cot²θ

= 1 + 1  [∵ cosec²θ − cot²θ = 1]

= 2