Category: Trigonometry

Question Number 25763 by amankumar last updated on 14/Dec/17 $$1+\cos {}^{2}2\theta =2(\cos {}^4\theta +\sin {}^4\theta )$$ Answered by ajfour last updated on 15/Dec/17 $$\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{2}\theta=\left(\mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{cos}\:^{\mathrm{2}}…

Question Number 25728 by ajfour last updated on 13/Dec/17 Commented by ajfour last updated on 13/Dec/17 $$Ifratioofareasof△PQRand$$$$△ABCbeindependentofa,b,c;$$$$findtheratio.$$ Commented by…

Question Number 90876 by john santu last updated on 26/Apr/20 $$\sqrt[3]{2\cos \left(\frac{\pi }{9}\right)}-\sqrt[3]{2\cos \left(\frac{2\pi }{9}\right)}-\sqrt[3]{2\cos \left(\frac{4\pi }{9}\right)}=?$$ Commented by john santu last updated on 26/Apr/20 $$Ramanujantheorem$$$${let}\:\alpha,\:\beta\:,\gamma\:{be}\:{a}\:{roots}\: \…

Question Number 156321 by cortano last updated on 10/Oct/21 $$\cos {}^4\left(\frac{\pi }{9}\right)+\cos {}^4\left(\frac{2\pi }{9}\right)+\cos {}^4\left(\frac{3\pi }{9}\right)+\cos {}^4\left(\frac{4\pi }{9}\right)=?$$ Commented by john_santu last updated on 10/Oct/21 $${ans}\::\:\frac{\mathrm{19}}{\mathrm{16}} \…

Question Number 90739 by ajfour last updated on 25/Apr/20 $$solveforxandy$$$$\tan {}^2\left[\pi (x+y)\right]+\cot {}^2\left[\pi (x+y)\right]$$$$=1+\sqrt{\frac{2x}{x^2+1}}$$ Commented by me2love2math last updated on…