Category: Trigonometry

Question Number 57001 by nisha sinah last updated on 28/Mar/19 $$constructananalyticfunctionf\left(z\right)whoserealpartis{e}^x\cos y$$ Commented by 121194 last updated on 28/Mar/19 $$f\left(z\right)=e^z$$$${e}^{{z}} ={e}^{{x}+{iy}}…

Question Number 122505 by aupo14 last updated on 17/Nov/20 Answered by MJS_new last updated on 17/Nov/20 $$t=\tan \frac{\theta }{2}$$$$5\frac{2t}{t^2+1}+\frac{t^2-1}{t^2+1}=\frac{t^2+1}{2t}$$$${t}^{\mathrm{4}}…

Question Number 56681 by Joel578 last updated on 21/Mar/19 $$\mathrm{Prove}\mathrm{that}$$$$\sin \mid x\mid ⩽\mid x\mid ⩽\tan \mid x\mid \mathrm{for}\mid x\mid <\frac{\pi }{2}$$ Commented by Abdo msup. last updated on 22/Mar/19 $$let\mid x\mid =tletprovethatsint⩽t⩽tantfor0⩽t<\frac{\pi }{2}$$$${let}\:{W}\left({x}\right)={t}−{sint}\:\Rightarrow{W}^{,}…

Question Number 122076 by peter frank last updated on 14/Nov/20 Answered by MJS_new last updated on 14/Nov/20 $$\mathrm{let}t=\tan A$$$$\frac{\mathrm{1}+{t}−\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}+{t}−\mathrm{1}}=\frac{\mathrm{1}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}−{t}}{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}+{t}+\mathrm{1}} \…

Question Number 187559 by Mingma last updated on 18/Feb/23 Answered by cortano12 last updated on 19/Feb/23 $$\frac{\sin x}{\sin y}.\frac{\cos y}{\cos x}=\frac{1}{3}\Rightarrow \frac{\tan x}{\tan y}=\frac{1}{3}$$$$3\tan x=\tan y$$$$\Rightarrow \tan (x+y)=\frac{4\tan x}{1-3\tan {}^{2}x}=\pm \sqrt{15}$$$$\Rightarrow\mathrm{2sin}\:{x}=\mathrm{sin}\:{y}\:;\:\mathrm{2cos}\:{x}=\mathrm{3cos}\:{y} \…