LET \[y=\FRAC{\tan x}{\tan 3x}=\frac{\tan x}{\frac{3\tan x-{{\tan }^{3}}x}{1-3{{\tan }^{2}}x}}\] \[y=\frac{1-3{{\tan }^{2}}x}{3-{{\tan }^{2}}x}=\frac{\frac{1}{3}-{{\tan }^{2}}x}{1-\frac{1}{3}.{{\tan }^{2}}x}\] Hence, y should never lie between \[\frac{1}{3}\]and 3 WHENEVER defined. "> LET \[y=\FRAC{\tan x}{\tan 3x}=\frac{\tan x}{\frac{3\tan x-{{\tan }^{3}}x}{1-3{{\tan }^{2}}x}}\] \[y=\frac{1-3{{\tan }^{2}}x}{3-{{\tan }^{2}}x}=\frac{\frac{1}{3}-{{\tan }^{2}}x}{1-\frac{1}{3}.{{\tan }^{2}}x}\] Hence, y should never lie between \[\frac{1}{3}\]and 3 WHENEVER defined. ">
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The value of \[\frac{\tan x}{\tan \,3x}\]whenever defined never lie between [Kurukshetra CEE 1998; IIT 1992]

Mathematics Trigonometric Identities in Mathematics . 7 months ago

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LET \[y=\FRAC{\tan x}{\tan 3x}=\frac{\tan x}{\frac{3\tan x-{{\tan }^{3}}x}{1-3{{\tan }^{2}}x}}\] \[y=\frac{1-3{{\tan }^{2}}x}{3-{{\tan }^{2}}x}=\frac{\frac{1}{3}-{{\tan }^{2}}x}{1-\frac{1}{3}.{{\tan }^{2}}x}\] Hence, y should never lie between \[\frac{1}{3}\]and 3 WHENEVER defined.
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Posted on 27 Aug 2024, this text provides information on Mathematics related to Trigonometric Identities in Mathematics. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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