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.


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