Sequence And Series Question 428
Question: Which one of the following options is correct?
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
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Three numbers a. b and c will be in GP. if $ b^{2}=ac $ . Only option [d] i.e. $ {{\tan }^{2}}30{}^\circ ,{{\tan }^{2}}45{}^\circ $ and $ {{\tan }^{2}}60{}^\circ $ are in GP. $ \because {{\tan }^{2}}30{}^\circ =\frac{1}{3} $ $ {{\tan }^{2}}45{}^\circ =1 $ and $ {{\tan }^{2}}60{}^\circ =3 $
$ \therefore ,{{\tan }^{2}}30{}^\circ ,{{\tan }^{2}}45{}^\circ $ and $ {{\tan }^{2}}60{}^\circ $ are in GP.
BETA
