sin (50° +θ) — cos (40° — θ) + tan 1°tan 10°tan 80°tan 89° =1

Question

Philoid · Accepted Answer

Consider L.H.S.

= sin (50° +θ) — cos (40° — θ) + tan 1° tan 10° tan 80° tan 89°

= sin ((90°-(40° - θ)) — cos (40° — θ) + (tan 1° tan 89°)(tan10° tan 80°)

= cos (40° - θ) - cos (40° - θ) + [tan 1° tan (90°-1°)][tan10° tan(90°-10°)]

= 0 + [(tan 1° cot 1°] [tan10° cot 10°]

= 0 + [1] × [1]

= 0 + 1 = 1 = R.H.S.

Hence, proved.