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Question
Show that: tan 10° tan 15° tan 75° tan 80° = 1.
Sum
Solution
L.H.S.
= tan 10° tan 15° tan 75° tan 80°
= tan (90° - 80°) tan (90° - 75°) tan 75° tan 80°
= cot 80° cot 75 ° tan 75° tan 80°
= (cot 80° tan 80°)(cot 75° tan 75°)
= (1)(1)
= 1
= R.H.S.
shaalaa.com
Complimentary Angles for Tangent ( Tan ) and Contangency ( Cot )
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