Category: Trigonometry

Question Number 144164 by bobhans last updated on 22/Jun/21 $$\mathrm{In}\mathrm{\Delta }\mathrm{ABC}\mathrm{given}\mathrm{a}=5,\mathrm{b}=7\mathrm{\&}\mathrm{c}=4.$$$$\mathrm{If}\measuredangle \mathrm{CAB}=\alpha \mathrm{then}\cot \left(\frac{1}{2}\alpha \right)=?$$ Answered by liberty last updated on 22/Jun/21 $$\cot \left(\frac{1}{2}\alpha \right)=\sqrt{\frac{\mathrm{s}(\mathrm{s}-\mathrm{a})}{(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})}}$$$$\mathrm{where}\:\mathrm{s}\:=\:\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{\mathrm{2}}=\frac{\mathrm{5}+\mathrm{7}+\mathrm{4}}{\mathrm{2}}=\mathrm{8} \…

Question Number 144139 by bobhans last updated on 22/Jun/21 Answered by liberty last updated on 22/Jun/21 Commented by EDWIN88 last updated on 22/Jun/21 $$\frac{\mathrm{4}}{\mathrm{R}}\:=\:\frac{\mathrm{8}}{\mathrm{12}+\mathrm{R}}\:\Rightarrow\frac{\mathrm{1}}{\mathrm{R}}=\frac{\mathrm{2}}{\mathrm{12}+\mathrm{R}}\:;\:\mathrm{R}=\mathrm{12} \…

Question Number 131492 by Ar Brandon last updated on 05/Feb/21 $${\sin }^4\frac{\pi }{16}+{\sin }^4\frac{3\pi }{16}+{\sin }^4\frac{5\pi }{16}+{\sin }^4\frac{7\pi }{16}$$ Answered by Dwaipayan Shikari last updated on 05/Feb/21…

Question Number 131301 by liberty last updated on 03/Feb/21 $${\cos }^{-1}\sqrt{{\mathrm{x}}^3-\mathrm{x}+1}+{\cos }^{-1}\sqrt{\mathrm{x}-{\mathrm{x}}^3}+{\cos }^{-1}\sqrt{1-\mid \mathrm{y}\mid }=\frac{2\pi }{3}$$$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{y}$$ Answered by EDWIN88 last updated on…

Question Number 131302 by EDWIN88 last updated on 03/Feb/21 $$Given\sin (\frac{\pi }{6}+{\tan }^{-1}\left(x\right))=\frac{13}{14}$$$$If{\tan }^{-1}\left(x\right)={\tan }^{-1}\left(\frac{a\sqrt{3}}{b}\right)then$$$$\frac{a+b}{2}=?$$ Answered by mr W last updated…