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If α = π/14 , then the value of (tan α tan 2α + tan 2α tan 4α + tan 4α tan α) is

If α = π/14 , then the value of (tan α tan 2α + tan 2α tan 4α + tan 4α tan α) is

Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
we see that α+2α+4α=pi/2
taking tan both sides and applying the formula tan(x+y+z)= [tanx+tany+tanz – tanxtanytanz]/[1 – (tanxtany+tanytanz+tanztanx)], we get
 [tanα+tan2α+tan4α – tanαtan2αtan4α]/[1 – (tanαtan2α+tan2αtan4α+tanαtan4α)]= not defined.
but this is possible only when the denominator is zero, ie
1 – (tanαtan2α+tan2αtan4α+tanαtan4α)=0
or 1= tanαtan2α+tan2αtan4α+tanαtan4α

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