Category: Trigonometry

Question Number 116891 by bemath last updated on 07/Oct/20 $$\mathrm{Proof}\mathrm{that}\frac{4(\cos {}^4\left(a\right)+\sin {}^4\left(a\right))}{\cos {}^4\left(a\right)-\sin {}^4\left(a\right)}=(3+\cos \left(4a\right))\sec \left(2a\right)$$ Answered by john santu last updated on 07/Oct/20 $$\Rightarrow\:\frac{\mathrm{4}\left\{\left(\mathrm{sin}\:^{\mathrm{2}}…

Question Number 116832 by bemath last updated on 07/Oct/20 $$\mathrm{If}19\sin 2\mathrm{x}=37\cos 2\mathrm{x}+38\sin {}^2\mathrm{x}$$$$\mathrm{then}\tan \mathrm{x}=\mathrm{\_}\mathrm{\_}$$ Answered by bobhans last updated on 07/Oct/20 $$\Rightarrow\mathrm{19}\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{37}\:\mathrm{cos}\:\mathrm{2x}+\mathrm{38sin}\:^{\mathrm{2}} \mathrm{x} \…

Question Number 116768 by bemath last updated on 06/Oct/20 $$\sin \left({4\sin }^{-1}\left(\mathrm{x}\right)\right)=\sin \left({2\sin }^{-1}\left(\mathrm{x}\right)\right)$$ Answered by bobhans last updated on 06/Oct/20 $$\mathrm{letting}{\sin }^{-1}\left(\mathrm{x}\right)=\mathrm{z}\Rightarrow \sin \mathrm{z}=\mathrm{x}$$$$\Rightarrow\:\mathrm{sin}\:\left(\mathrm{4z}\right)\:=\:\mathrm{sin}\:\left(\mathrm{2z}\right)\:…

Question Number 116630 by bobhans last updated on 05/Oct/20 $$\mathrm{Given}\mathrm{cosec}\mathrm{x}+\cot \mathrm{x}=\mathrm{p},\mathrm{find}\mathrm{the}$$$$\mathrm{value}\mathrm{of}\mathrm{cosec}\mathrm{x}=?$$ Answered by TANMAY PANACEA last updated on 05/Oct/20 $$\mathrm{1}+{cot}^{\mathrm{2}} {x}={cosec}^{\mathrm{2}} {x}…

Question Number 50996 by rahul 19 last updated on 23/Dec/18 $$Findtheminimumvalueof$$$$f\left(x\right)={9\tan }^2\theta +{4\cot }^2\theta ?$$ Commented by rahul 19 last updated on 23/Dec/18…