Category: Trigonometry

Question Number 78427 by Chi Mes Try last updated on 17/Jan/20 $$pleaseineediturgently$$$$$$$$showthatthemidpointofthehypotenuse$$$$ofarighttriangleisequidistantfromitsvertices$$ Answered by MJS last updated…

Question Number 143958 by bobhans last updated on 20/Jun/21 Answered by bramlex last updated on 20/Jun/21 $$\Rightarrow \{\begin{array}{l}\sin {}^2\alpha +2\sin \alpha \sin \beta +\sin {}^2\beta =9p\\ \cos {}^2\alpha +2\cos \alpha \cos \beta +\cos {}^2\beta =9q\end{array}$$$$\iff 2+2\cos (\alpha -\beta )=9(p+q)$$$$\Leftrightarrow\:\mathrm{2cos}\:\left(\alpha−\beta\right)=\mathrm{9}\left({p}+{q}\right)−\mathrm{2}…

Question Number 143923 by Sravanth last updated on 19/Jun/21 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}\left[{\sin }^{-1}\left(\sin \left(\frac{2\pi }{3}\right)\right)\right]?$$ Commented by mr W last updated on 19/Jun/21 $${\sin }^{-1}\left(\sin \left(\frac{2\pi }{3}\right)\right)=\frac{\pi }{3}$$…

Question Number 143897 by liberty last updated on 19/Jun/21 Answered by bobhans last updated on 19/Jun/21 $$\sin {}^2\frac{\pi }{8}+\cos {}^2\frac{\pi }{8}+\cos {}^2\frac{5\pi }{8}+\sin {}^2\frac{5\pi }{8}=2$$ Terms of…

Question Number 143857 by gsk2684 last updated on 19/Jun/21 $$\mathrm{if}{\cos }^4\theta \sec {}^2\alpha ,\frac{1}{2},{\sin }^4\theta {\mathrm{cosec}}^2\alpha$$$$\mathrm{are}\mathrm{in}\mathrm{A}.\mathrm{P}.\mathrm{then}$$$${\cos }^8\theta {\sec }^6\alpha ,\frac{1}{2},{\sin }^8\theta {\mathrm{cosec}}^6\alpha$$$$\mathrm{are}\:\mathrm{in}\:\mathrm{which}\:\mathrm{progression}? \…