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Category: Trigonometry

If-ta4-1-find-the-values-of-

Question Number 194327 by pete last updated on 03/Jul/23 $$\mathrm{If}\:\mathrm{ta4}\theta\:=\:\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\theta. \\ $$ Answered by MikeH last updated on 03/Jul/23 $$\mathrm{tan}\:\mathrm{4}\theta\:=\:\mathrm{1}\: \\ $$$$\Rightarrow\:\mathrm{4}\theta\:=\:\pi{n}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\pi \\ $$$$\Rightarrow\:\theta\:=\:\frac{\mathrm{1}}{\mathrm{4}}\pi{n}\:+\:\frac{\mathrm{1}}{\mathrm{16}}\pi \\…

Question-194315

Question Number 194315 by cortano12 last updated on 03/Jul/23 $$\:\:\:\:\: \\ $$ Answered by Frix last updated on 03/Jul/23 $$\mathrm{This}\:\mathrm{can}\:\mathrm{be}\:\mathrm{transformed}\:\mathrm{to}\:\left[{s}=\mathrm{sin}\:{x}\right]: \\ $$$${s}^{\mathrm{4}} +\frac{{s}^{\mathrm{3}} }{\mathrm{2}}−{s}^{\mathrm{2}} −\frac{{s}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{16}}=\mathrm{0}…

Question-194304

Question Number 194304 by 281981 last updated on 02/Jul/23 Answered by cortano12 last updated on 03/Jul/23 $$\:\:\:\:\mathrm{sin}\:\left(\mathrm{A}+\mathrm{B}\right)\:\mathrm{cos}\:\left(\mathrm{A}+\mathrm{B}\right)\:\mathrm{sin}\:\left(\mathrm{A}−\mathrm{B}\right)\:\mathrm{cos}\:\left(\mathrm{A}−\mathrm{B}\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\mathrm{sin}\:\left(\mathrm{2A}+\mathrm{2B}\right)\:\mathrm{sin}\:\left(\mathrm{2A}−\mathrm{2B}\right)=\:\mathrm{2} \\ $$$$\:\:\:\underbrace{\boldsymbol{{A}}} \\ $$ Commented by…