A) \[si{{n}^{2}}30{}^\circ ,\text{ }si{{n}^{2}}45{}^\circ ,\text{ }si{{n}^{2}}60{}^\circ \] are in GP
B) \[co{{s}^{2}}30{}^\circ ,\text{ }co{{s}^{2}}45{}^\circ ,\text{ }co{{s}^{2}}60{}^\circ \] are in GP
C) \[co{{t}^{2}}30{}^\circ ,\text{ }co{{t}^{2}}45{}^\circ ,\text{ }co{{t}^{2}}60{}^\circ \] are in GP
D) \[ta{{n}^{2}}30{}^\circ ,\text{ }ta{{n}^{2}}45{}^\circ ,\text{ }ta{{n}^{2}}60{}^\circ \] are in GP
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.
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