Category: Trigonometry

Question Number 21060 by NECx last updated on 11/Sep/17 $$\mathrm{write}\sin 1°\mathrm{in}\mathrm{surd}\mathrm{form}$$$$$$$$$$$$\mathrm{please}\mathrm{show}\mathrm{workings}.$$ Commented by NECx last updated on 11/Sep/17…

Question Number 86550 by DuDono last updated on 29/Mar/20 $$\mathrm{show}\mathrm{that}$$$$\tan {}^{-1}x=\frac{\ln (-x^2+2ix+1)-\ln (x^2+1)}{2i}$$ Commented by john santu last updated on 29/Mar/20…

Question Number 152035 by puissant last updated on 25/Aug/21 $$Showthat2sin7\theta cos3\theta =sin10\theta +sin4\theta .$$ Answered by som(math1967) last updated on 25/Aug/21 $$2sinA\mathit{c}\mathit{o}\mathit{s}\mathit{B}=\mathit{s}\mathit{i}\mathit{n}(\mathit{A}+\mathit{B})+\mathit{s}\mathit{i}\mathit{n}(\mathit{A}-\mathit{B})$$$$\therefore 2\mathit{s}\mathit{i}\mathit{n}7\mathit{\theta }\mathit{c}\mathit{o}\mathit{s}3\mathit{\theta }=\mathit{s}\mathit{i}\mathit{n}(7\mathit{\theta }+3\mathit{\theta })+\mathit{s}\mathit{i}\mathit{n}(7\mathit{\theta }-3\mathit{\theta })$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\boldsymbol{{sin}}\mathrm{10}\boldsymbol{\theta}+{s}\boldsymbol{{in}}\mathrm{4}\boldsymbol{\theta} \…

Question Number 86476 by DuDono last updated on 28/Mar/20 $$\mathrm{show}\mathrm{that}$$$${\sin }^{-1}\alpha =-i\ln (\alpha \pm \sqrt{{\alpha }^2-1})-\frac{\pi }{2}$$ Commented by MJS last updated on 28/Mar/20 $$\mathrm{the}\:\mathrm{path}\:\mathrm{is}\:\mathrm{this}: \…

Question Number 151959 by john_santu last updated on 24/Aug/21 Answered by iloveisrael last updated on 24/Aug/21 $${\left(\sin {}^{2}x\right)}^3+{\left(\cos {}^{2}x\right)}^3=\frac{1}{4}$$$$\Rightarrow\left(\mathrm{1}\right)\left(\mathrm{sin}\:^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}−\left(\mathrm{sin}\:{x}\mathrm{cos}\:{x}\right)^{\mathrm{2}}…