Category: Trigonometry

Question Number 126954 by bramlexs22 last updated on 25/Dec/20 $$\cos \left(\frac{5\pi }{18}\right)+\cos \left(\frac{7\pi }{18}\right)+\cos \left(\frac{17\pi }{18}\right)=?$$ Answered by Dwaipayan Shikari last updated on 25/Dec/20 $$2cos\left(\frac{12\pi }{36}\right)cos\left(\frac{\pi }{18}\right)+cos\left(\frac{17\pi }{18}\right)$$$$=cos\left(\frac{\pi }{18}\right)+cos\left(\frac{17\pi }{18}\right)=2cos\left(\frac{\pi }{2}\right)cos\left(\frac{8\pi }{18}\right)=0$$…

Question Number 192346 by Rupesh123 last updated on 15/May/23 Answered by som(math1967) last updated on 15/May/23 $${\left(\frac{2cos30cos20+cos70+cos(180-70)}{cos20}\right)}^8$$$$={\left(\frac{\sqrt{3}cos20+\cos 70-\cos 70}{cos20}\right)}^8$$$$={\left(\frac{\sqrt{3}cos20}{cos20}\right)}^8$$$$=\left(\sqrt{\mathrm{3}}\right)^{\mathrm{8}} =\mathrm{81} \…

Question Number 192278 by manxsol last updated on 13/May/23 $$S=arctan\left(\frac{2}{1^2}\right)+artan\left(\frac{2}{2^2}\right)+\dots \dots ..$$ Commented by Frix last updated on 14/May/23 $$\mathrm{As}\mathrm{I}\mathrm{posted}\mathrm{before}\left(\mathrm{but}\mathrm{it}\mathrm{was}\mathrm{deleted}\right):$$$$\mathrm{I}\:\mathrm{approximated}\:\mathrm{it}\:\mathrm{using}\:\mathrm{software}\:\mathrm{and}\:\mathrm{got} \…

Question Number 61157 by Askash last updated on 29/May/19 $$if$$$$tan5\theta +tan4\theta =1$$$$find3\theta$$$$$$$$$$ Commented by mr W last…

Question Number 126610 by bramlexs22 last updated on 22/Dec/20 $$Given\{\begin{array}{l}\cos x+\sin x=p\\ \sec x+\csc x=q\end{array}$$$$p\ne q.Find\frac{\cos {}^{2}x}{2-2\sin {}^{2}x-\mathrm{cs}{c}^{2}x}.$$ Answered by liberty last updated on 22/Dec/20 $$\:{q}\:=\:\left(\frac{\mathrm{cos}\:{x}+\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}\right)\Rightarrow{q}^{\mathrm{2}}…