Question

Evaluate: sin (50 0 +Θ) –cos (40 0 -Θ) + tan 1 0 tan 10 0 tan 20 0 tan 70 0 tan 80 0 tan 89 0 + sec (90 – Θ) . cosec Θ – tan(90 – Θ) . cot Θ

Answer 1

sin(50°+θ)-cos(40-θ)+tan 1×tan 10 ×tan 20× tan 70×tan 80×tan 89+sec(90-θ) × cosec θ-tan(90-θ)×cot θ
=cos(40-θ)-cos(40-θ)+cot 89 ×cot 80× cot 70×tan 70×tan 80×tan 89+cosecθ× cosecθ-cotθ× cot θ
=1+1/tan 89×1/tan 80×1/tan 70×tan 70×tan 80×tan 89+cosec²θ -cot²θ
=1+1+1 [ cosec²θ-cot²θ=1]
=3