If tan(π/9), x, tan(7π/18) are in arithmetic progression and tan(π/9), y, tan(5π/18) are also in arithmetic progression, then |x - 2y| is equal to :
If tan(π/9), x, tan(7π/18) are in arithmetic progression and tan(π/9), y, tan(5π/18) are also in arithmetic progression, then |x - 2y| is equal to :
Option 1 -
1
Option 2 -
0
Option 3 -
4
Option 4 -
3
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1 Answer
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Correct Option - 1
Detailed Solution:2x=tan (π/9)+tan (7π/18)
=sin (π/9+7π/18) / cos (π/9)cos (7π/18)
=sin (π/2) / cos (π/9)cos (7π/18)
=1 / cos (π/9)cos (7π/18)
=1 / cos (π/9)sin (π/2−7π/18)
=1 / cos (π/9)sin (π/9)
⇒x=1 / 2cos (π/9)sin (π/9)
=1 / sin (2π/9)=cosec (2π/9)Again 2y=tan (π/9)+tan (5π/18)
⇒2y=sin (π/9+5π/18) / cos (π/9)cos (5π/18)
=sin (7π/18) / sin (π/2−π/9)sin (π/2−5π/18)
=sin (7π/18) / sin (7π/18)sin (4π/18) = cosec (2π/9)
⇒|x−2y|=0
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