Find the value off the following:

(sin 50° + θ)- cos (40° - θ) + tan 1°. tan 10° tan 20°. tan 70°. tan 80°. tan 89°

(sin 50° + θ)- cos (40° -θ) + tan 1° tan 10° tan 20° tan 70° tan 80° tan 89°

= cos {90° -(50° + θ)} - cos (40° -θ)+ cot(90° - 1°) tan (90° - 10°) cot(90° - 20°) tan 70° tan 80° tan 89° [∵ Sin θ = cos (90° - θ) & tan θ = cot (90° - θ)]

= cos (40° -θ) - cos (40° -θ) + cot89° cot80° cot70° tan 70° tan 80° tan 89°

= 1