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Question: Answered & Verified by Expert
Which one of the following options is correct?
MathematicsSequences and SeriesNDANDA 2011 (Phase 1)
Options:
  • A $\sin ^{2} 30^{\circ}, \sin ^{2} 45^{\circ}, \sin ^{2} 60^{\circ}$ are in GP
  • B $\cos ^{2} 30^{\circ}, \cos ^{2} 45^{\circ}, \cos ^{2} 60^{\circ}$ are in GP
  • C $\cot ^{2} 30^{\circ}, \cot ^{2} 45^{\circ}, \cot ^{2} 60^{\circ}$ are in GP
  • D $\tan ^{2} 30^{\circ}, \tan ^{2} 45^{\circ}, \tan ^{2} 60^{\circ}$ are in GP
Solution:
1732 Upvotes Verified Answer
The correct answer is: $\tan ^{2} 30^{\circ}, \tan ^{2} 45^{\circ}, \tan ^{2} 60^{\circ}$ are in GP
Three numbers a, b and c will be in G.P. if $b^{2}=a c$. Only option (d) i.e. $\tan ^{2} 30^{\circ}, \tan ^{2} 45^{\circ}$ and $\tan ^{2} 60^{\circ}$ are
in GP.
$\because \quad \tan ^{2} 30^{\circ}=\frac{1}{3}$
$\tan ^{2} 45^{\circ}=1$
and $\tan ^{2} 60^{\circ}=3$
$\tan ^{2} 30^{\circ}, \tan ^{2} 45^{\circ}$ and $\tan ^{2} 60^{\circ}$ are in G.P.

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