Category: Trigonometry

Question Number 193669 by Rupesh123 last updated on 17/Jun/23 Answered by AST last updated on 18/Jun/23 $$cos(x+y)+isin(x+y)=e^{i(x+y)}=e^{ix}{e}^{iy}$$$$=(cos\left(x\right)+isin\left(x\right))(cos\left(y\right)+isin\left(y\right))$$$$=cos\left(x\right)cos\left(y\right)-sin\left(x\right)cos\left(y\right)+icos\left(x\right)sin\left(y\right)+isin\left(x\right)cos\left(y\right)$$$${Comparing}\:{real}\:{parts}…

Question Number 193533 by horsebrand11 last updated on 16/Jun/23 $$\mathrm{If}\cot \mathrm{x}-\tan \mathrm{x}=4\mathrm{then}$$$$\cot {}^2+\frac{2}{\sin 2\mathrm{x}}-\tan {}^2\mathrm{x}=?$$ Answered by MM42 last updated on 16/Jun/23 $$\mathrm{1}−{tan}^{\mathrm{2}} {x}=\mathrm{4}{tanx}\Rightarrow{tan}^{\mathrm{2}}…

Question Number 193464 by Mingma last updated on 14/Jun/23 Commented by Frix last updated on 14/Jun/23 $$\mathrm{For}\mathrm{any}\mathrm{triangle}$$$$r_n=\frac{c\delta }{2((a+b+c)c+(n-1)\delta )}$$$$[\delta =\sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}$$$$\mathrm{For}\:\mathrm{a}\:\mathrm{rectangular}\:\mathrm{triangle}\:\mathrm{with}\:{c}=\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}}…

Question Number 193458 by SAMIRA last updated on 14/Jun/23 $$\underset{x\to 0}{\lim }\left(\frac{1-\cos \left(\mathrm{x}\right)}{\mathrm{x}\sin \left(\mathrm{x}\right)}\right)=???$$ Commented by aba last updated on 14/Jun/23 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{xsin}\left(\mathrm{x}\right)}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }×\frac{\mathrm{x}}{\mathrm{sin}\left(\mathrm{x}\right)}=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{1}=\mathrm{0}.\mathrm{5} \…

Question Number 193423 by mustafazaheen last updated on 13/Jun/23 $$\mathrm{when}\tan \frac{\theta }{2}=\frac{1}{\mathrm{a}}$$$$\mathrm{then}\mathrm{find}\cos \theta =?\mathrm{from}\mathrm{the}\mathrm{a}$$ Answered by AST last updated on 13/Jun/23 $${tan}\left(\frac{\theta}{\mathrm{2}}+\frac{\theta}{\mathrm{2}}\right)=\frac{\mathrm{2}{tan}\left(\frac{\theta}{\mathrm{2}}\right)}{\mathrm{1}−{tan}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right)}\Rightarrow{tan}\left(\theta\right)=\frac{\mathrm{2}{a}}{{a}^{\mathrm{2}} −\mathrm{1}} \…