Category: Trigonometry

Question Number 103643 by bemath last updated on 16/Jul/20 $$if\sin x+\cos x=\frac{5}{6}$$$$then\frac{1}{\sin x}+\frac{1}{\cos x}?$$ Answered by Dwaipayan Shikari last updated on 16/Jul/20 $$\left({sinx}+{cosx}\right)^{\mathrm{2}} −\mathrm{2}{sinxcosx}=\mathrm{1} \…

Question Number 103459 by bemath last updated on 15/Jul/20 $$whatarethecomplexsolution\tan$$$$\left(z\right)=-2?$$ Commented by mr W last updated on 15/Jul/20 $${z}={k}\pi−\mathrm{tan}^{−\mathrm{1}} \mathrm{2} \…

Question Number 103314 by Ar Brandon last updated on 14/Jul/20 $$\mathrm{Linearise}{\cos }^{2(\mathrm{p}-1)}\left(\mathrm{t}\right)$$ Answered by OlafThorendsen last updated on 14/Jul/20 $$\mathrm{cos}^{\mathrm{2}\left({p}−\mathrm{1}\right)} \left({t}\right)\:=\:\left[\frac{{e}^{{it}} +{e}^{−{it}} }{\mathrm{2}}\right]^{\mathrm{2}\left({p}−\mathrm{1}\right)}…

Question Number 37733 by kunal1234523 last updated on 17/Jun/18 $$\mathrm{Prove}\mathrm{that}\mathrm{the}\mathrm{equation}\sin \theta =x+\frac{1}{x}$$$$\mathrm{is}\mathrm{impossible}\mathrm{if}x\mathrm{be}\mathrm{real}.$$ Answered by MrW3 last updated on 17/Jun/18 $$ifx>0:$$$$\mathrm{sin}\:\theta={x}+\frac{\mathrm{1}}{{x}}=\left(\sqrt{{x}}−\frac{\mathrm{1}}{\:\sqrt{{x}}}\right)^{\mathrm{2}} +\mathrm{2}\geqslant\mathrm{2}…

Question Number 168664 by cortano1 last updated on 15/Apr/22 $$\{\begin{array}{l}8\cos x-8\sin x=3\\ 55\tan x+\frac{55}{\tan x}=?\end{array}$$ Answered by greogoury55 last updated on 15/Apr/22 $${(8\cos x-8\sin x)}^2=9$$$$64-64\sin 2x=9$$$$\Rightarrow\mathrm{55}\:=\:\mathrm{64sin}\:\mathrm{2}{x}…