Category: Trigonometry

Question Number 128130 by physicstutes last updated on 04/Jan/21 $$\mathrm{prove}\mathrm{that}$$$$\sin (2x+2h)-\sin 2x=2\cos (2x+h)\sin h$$ Answered by Olaf last updated on 04/Jan/21 $$\sin a-\sin b=2\sin \left(\frac{a-b}{2}\right)\cos \left(\frac{a+b}{2}\right)\left(1\right)$$$${a}\:=\:\mathrm{2}{x}+\mathrm{2}{h}\:\mathrm{and}\:{b}\:=\:\mathrm{2}{x} \…

Question Number 128068 by benjo_mathlover last updated on 04/Jan/21 $$\mathrm{Given}{25\mathrm{x}}^2-30\mathrm{x}+7=0\mathrm{has}\mathrm{the}$$$$\mathrm{roots}\mathrm{are}\cos \alpha \mathrm{and}\cos \beta .\mathrm{If}\cos \alpha -\cos \beta >0$$$$\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\tan \left(\frac{\alpha +\beta }{2}\right).\tan \left(\frac{\alpha -\beta }{2}\right)=?$$ Answered by bemath last updated on 04/Jan/21 $$\:\mathrm{let}\:\frac{\alpha+\beta}{\mathrm{2}}=\mathrm{x}\:\wedge\:\frac{\alpha−\beta}{\mathrm{2}}=\mathrm{y}…

Question Number 62431 by rajesh4661kumar@gamil.com last updated on 21/Jun/19 Answered by tanmay last updated on 21/Jun/19 $${asin}^2\theta +{bcos}^2\theta =c$$$${asin}^2\theta +b(1-{sin}^2\theta )=c$$$${sin}^{\mathrm{2}}…

Question Number 62347 by rajesh4661kumar@gamil.com last updated on 20/Jun/19 Answered by Kunal12588 last updated on 20/Jun/19 $$\frac{csc\theta -sin\theta }{sec\theta -cos\theta }=\frac{a^3}{b^3}$$$$\Rightarrow{cot}\:\theta\:\frac{\mathrm{1}−{sin}^{\mathrm{2}} \theta}{\mathrm{1}−{cos}^{\mathrm{2}} \theta}=\frac{{a}^{\mathrm{3}} }{{b}^{\mathrm{3}} }…

Question Number 127835 by bemath last updated on 02/Jan/21 $$\mathrm{If}\underset{\mathrm{k}=1}{\prod ^{10}}\cos \left(\frac{\mathrm{k}\pi }{11}\right)=-2^{\mathrm{n}},\mathrm{then}\mathrm{n}=?$$$$$$ Answered by liberty last updated on 02/Jan/21 $$\:\mathrm{let}\:\mathrm{Y}\:=\:\mathrm{cos}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{3x}\:\mathrm{cos}\:\mathrm{4x}\:…