Category: Trigonometry

Question Number 108145 by bemath last updated on 15/Aug/20 $$\frac{⊚\mathcal{B}e\mathcal{M}ath⊚}{\mathrm{\Pi }}$$$$\left(1\right)\cos {}^2\left(\frac{x}{4}\right)>\frac{\sqrt{2}}{2}+\sin {}^2\left(\frac{x}{4}\right)$$$$\left(2\right)\int \sqrt{\frac{1+x}{1-x}}dx$$$$\left(3\right)\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}\frac{\sqrt{\tan x}}{{(\cos x+\sin x)}^2}dx$$ Commented by…

Question Number 42520 by gyugfeet last updated on 27/Aug/18 $${cos}^{3}A.sin3A+sinA.cos3A=\frac{3}{4}sin4A$$ Answered by tanmay.chaudhury50@gmail.com last updated on 27/Aug/18 $$cos3A=\frac{4{cos}^{3}A-3cosA}{}$$$$\left(\frac{\mathrm{3}{cosA}+{cos}\mathrm{3}{A}}{\mathrm{4}}\right){sin}\mathrm{3}{A}+{sinAcos}\mathrm{3}{A} \…

Question Number 107978 by anonymous last updated on 13/Aug/20 $$ontheintervalof[0,\pi ]solve$$$${\tan }^{2}x+3secx=-3$$$$$$ Answered by bemath last updated on 14/Aug/20 $$\:\:\:\frac{\bullet\mathscr{B}{emath}\bullet}{\mathscr{C}{ooll}}…

Question Number 107932 by bemath last updated on 13/Aug/20 $$\frac{\mathbb{B}e\mathbb{M}ath}{\bullet }$$$$Given\{\begin{array}{l}\tan (x-y)=\frac{3}{4}\\ \tan x=2\end{array}$$$$find\tan y?$$ Commented by mnjuly1970 last updated on 13/Aug/20 $$\:{excellent}. \…

Question Number 107900 by bemath last updated on 13/Aug/20 $$\frac{\mathrm{\Sigma }\mathcal{B}e\mathcal{M}ath\mathrm{\Sigma }}{\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}}$$$$Given\tan x-\sec x=\vartheta$$$$then\sin x=?$$ Answered by bemath last updated on 13/Aug/20 $$\frac{\mathrm{sin}\:{x}−\mathrm{1}}{\mathrm{cos}\:{x}}\:=\:\upsilon\:\Rightarrow\:\mathrm{sin}\:{x}−\mathrm{1}=\upsilon\:\mathrm{cos}\:{x}\:…\left(\mathrm{1}\right) \…