Category: Trigonometry

Question Number 54472 by Tawa1 last updated on 04/Feb/19 $$\mathrm{If}\mathrm{A},\mathrm{B},\mathrm{C}\mathrm{are}\mathrm{angle}\mathrm{of}\mathrm{a}\mathrm{triangle},\mathrm{show}\mathrm{that}$$$$\mathrm{tanA}+\mathrm{tanB}+\mathrm{tanC}=\mathrm{tanA}\mathrm{tanB}\mathrm{tanC}$$ Answered by math1967 last updated on 04/Feb/19 $$A+B+C=\pi$$$$\Rightarrow{A}+{B}=\pi−{C} \…

Question Number 185511 by mathlove last updated on 23/Jan/23 Answered by Frix last updated on 23/Jan/23 $$\frac{1}{2-\sqrt{3}}=2+\sqrt{3}=t$$$$t^{-\cos x}=t^{\sin x}$$$$-\cos x=\sin x$$$$\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}=−\mathrm{1} \…

Question Number 119919 by bramlexs22 last updated on 28/Oct/20 $$\sin 70°\cos 50°+\sin 260°\cos 280°=?$$ Answered by bobhans last updated on 28/Oct/20 $$\iff \sin 70°\cos 50°+(-\cos 10°)\left(\sin 10°\right)=$$$$\frac{1}{2}(\sin 120°+\sin 20°)-\frac{1}{2}\sin 20°=$$$$\:\:\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{3}}\:=\:\frac{\sqrt{\mathrm{3}}}{\mathrm{4}} \…

Question Number 185320 by mathlove last updated on 20/Jan/23 Answered by SEKRET last updated on 20/Jan/23 $$\mathbf{sin}\left(2\mathbf{a}\right)=2\mathbf{sin}\left(\mathbf{a}\right)\mathbf{cos}\left(\mathbf{a}\right)$$ Answered by SEKRET last updated on…

Question Number 54156 by Tawa1 last updated on 30/Jan/19 $$\mathrm{Please}\mathrm{sirs},\mathrm{How}\mathrm{is},-\cot \left(\alpha \right)=\tan (\frac{1}{2}\pi +\alpha )????$$ Commented by turbo msup by abdo last updated on 30/Jan/19 $$tan(\frac{\pi }{2}+\alpha )=\frac{sin(\frac{\pi }{2}+\alpha )}{cos(\frac{\pi }{2}+\alpha )}$$$$=\frac{{cos}\alpha}{−{sin}\alpha}\:=−\frac{\mathrm{1}}{{tan}\alpha}\:=−{cotan}\alpha\:.…