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If-tan-i-cos-isin-prove-that-n-2-4-and-1-2-log-tan-4-2-

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Question Number 168118 by Mastermind last updated on 03/Apr/22 $${If}\:{tan}\left(\theta+{i}\phi\right)={cos}\alpha+{isin}\alpha,\: \\ $$$${prove}\:{that}\::\:\theta=\frac{{n}\Pi}{\mathrm{2}}+\frac{\Pi}{\mathrm{4}}\:{and}\:\phi=\frac{\mathrm{1}}{\mathrm{2}}{log}\:{tan}\left(\frac{\Pi}{\mathrm{4}}+\frac{\alpha}{\mathrm{2}}\right) \\ $$ Answered by mathsmine last updated on 05/Apr/22 $${tan}\left(\theta+{i}\emptyset\right)=\frac{{tan}\left(\theta\right)+{tan}\left({i}\emptyset\right)}{\mathrm{1}−{tan}\left(\theta\right){tan}\left({i}\emptyset\right)} \\ $$$${tan}\left({ix}\right)={ith}\left({x}\right) \\…

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If-a-b-c-a-b-b-c-a-b-c-c-a-b-c-a-and-a-b-c-0-then-which-of-the-following-is-true-1-a-b-c-2-a-b-c-3-a-b-c-4-a-b-c-

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Question Number 37037 by jayanta11 last updated on 08/Jun/18 $${If}\:\frac{{a}+{b}−{c}}{{a}+{b}}\:=\:\frac{{b}+{c}−{a}}{{b}+{c}}\:=\frac{{c}+{a}−{b}}{{c}+{a}}\:{and}\: \\ $$$$\mathrm{a}+\mathrm{b}+\mathrm{c}\:\neq\:\mathrm{0}\:{then}\:{which}\:{of}\:{the}\:{following} \\ $$$$\left.{i}\left.{s}\:{true}\:\mathrm{1}\right)\:{a}=−{b}={c}\:\mathrm{2}\right)−{a}=−{b}={c}\: \\ $$$$\left.\mathrm{3}\left.\right)\:\mathrm{a}=\mathrm{b}=\mathrm{c}\:\mathrm{4}\right)\:\mathrm{a}=\mathrm{b}\neq{c} \\ $$ Answered by math1967 last updated on 08/Jun/18…

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Question-102544

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Question Number 102544 by 175mohamed last updated on 09/Jul/20 Answered by Rio Michael last updated on 10/Jul/20 $$\mathrm{for}\:{p}\:>\:\mathrm{1},\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{p}} }\:\mathrm{is}\:\mathrm{convergent}\:\Rightarrow\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{n}^{\mathrm{2}} }}\:\mathrm{diverges} \\…

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