Question Number 178 by 123456 last updated on 14/Dec/14 $$\mathrm{proof}\:\mathrm{that} \\ $$$$\mid\mathrm{sin}\:\mathrm{1sin}\:\mathrm{2}…\mathrm{sin}\:{n}\mid\leqslant\mathrm{sin}\:\frac{\pi}{{n}}\mathrm{sin}\:\frac{\mathrm{2}\pi}{{n}}…\mathrm{sin}\:\frac{\left({n}−\mathrm{1}\right)\pi}{{n}} \\ $$$$\mathrm{for}\:\forall{n}\in\mathbb{N}\backslash\left\{\mathrm{0},\mathrm{1}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131230 by Fikret last updated on 02/Feb/21 $$\frac{{sin}\mathrm{5}}{{cos}\mathrm{0}.{cos}\mathrm{5}}+\frac{{sin}\mathrm{5}}{{cos}\mathrm{5}.{cos}\mathrm{10}}+\:\:.\:\:.\:\:.\:\:+\frac{{sin}\mathrm{5}}{{cos}\mathrm{55}.{cos}\mathrm{60}}\:=? \\ $$ Answered by mr W last updated on 02/Feb/21 $${example}: \\ $$$$\mathrm{sin}\:\mathrm{5}=\mathrm{sin}\:\left(\mathrm{10}−\mathrm{5}\right)=\mathrm{sin}\:\mathrm{10}\:\mathrm{cos}\:\mathrm{5}−\mathrm{cos}\:\mathrm{10}\:\mathrm{sin}\:\mathrm{5} \\ $$$$\frac{\mathrm{sin}\:\mathrm{5}}{\mathrm{cos}\:\mathrm{5}\:\mathrm{cos}\:\mathrm{10}}=\mathrm{tan}\:\mathrm{10}−\mathrm{tan}\:\mathrm{5}…
Question Number 149 by rajabhay last updated on 25/Jan/15 $$\mathrm{if}\:\mathrm{tan}\:\mathrm{A}=\sqrt{\mathrm{2}}−\mathrm{1}\:\mathrm{then}\:\mathrm{find} \\ $$$$\frac{\mathrm{tan}\:\mathrm{A}}{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \:{A}}\:=\:? \\ $$ Answered by prakash jain last updated on 12/Dec/14 $$\mathrm{tan}^{\mathrm{2}} \mathrm{A}=\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 105 by mr.guddukr@gmail.com last updated on 25/Jan/15 $${sin}\mathrm{5}\theta=\:? \\ $$ Answered by mreddy last updated on 03/Dec/14 $$\mathrm{sin}\:\mathrm{2}\theta=\mathrm{2sin}\:\theta\mathrm{cos}\:\theta \\ $$$$\mathrm{cos}\:\mathrm{2}\theta=\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \theta \\ $$$$\mathrm{sin}\:\mathrm{3}\theta=\mathrm{sin}\:\left(\mathrm{2}\theta+\theta\right)=\mathrm{2sin}\:\theta\mathrm{cos}^{\mathrm{2}}…
Question Number 58 by abyaya last updated on 25/Jan/15 $${sin}\mathrm{450}+{cos}\mathrm{450} \\ $$ Answered by kader last updated on 17/Nov/14 $$\mathrm{sin}\:\left(\mathrm{360}+\mathrm{90}\right)+\mathrm{cos}\:\left(\mathrm{360}+\mathrm{90}\right) \\ $$$$\mathrm{sin}\:\mathrm{90}+\mathrm{cos}\:\mathrm{90} \\ $$$$\mathrm{1}+\mathrm{0}=\mathrm{1} \\…
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Question Number 131097 by dw last updated on 01/Feb/21 $${Determine}\:{the}\:{value}\:{of}\:\frac{{S}}{\pi},\:{if}\:{S}\:{is}\:{the}\:{sum},\:{in}\:{radians}, \\ $$$${all}\:{equation}\:{solutions}\:{contained}\:{in}\:{the}\:{interval}\:\left[\mathrm{0},\mathrm{14}\pi\right]. \\ $$$$ \\ $$$${the}\:{equation}\:{is}: \\ $$$${cos}\left({x}\right)+{cos}^{\mathrm{5}} \left({x}\right)+{cos}\left(\mathrm{7}{x}\right)=\mathrm{3} \\ $$ Answered by MJS_new last…
Question Number 19 by user1 last updated on 25/Jan/15 $$\mathrm{Let}\:\theta\:\mathrm{be}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{the}\:\mathrm{regression} \\ $$$$\mathrm{line}\:\mathrm{of}\:{y}\:\mathrm{on}\:{x}\:\mathrm{and}\:\mathrm{the}\:\mathrm{regression}\:\mathrm{line}\:\mathrm{of} \\ $$$${x}\:\mathrm{on}\:{y}.\:\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{tan}\:\theta=\left\{\frac{\left(\mathrm{1}−{r}^{\mathrm{2}} \right)}{{r}}×\frac{\sigma_{{x}} ×\sigma_{{y}} }{\left(\sigma_{{x}} ^{\mathrm{2}} +\sigma_{{y}} ^{\mathrm{2}} \right)}\right\} \\ $$…
Question Number 13010 by tawa tawa last updated on 10/May/17 Answered by sandy_suhendra last updated on 10/May/17 $$\mathrm{BC}\:=\:\sqrt{\mathrm{5}^{\mathrm{2}} −\left(\mathrm{7}−\mathrm{4}\right)^{\mathrm{2}} }\:=\:\mathrm{4}\:\mathrm{cm} \\ $$$$\mathrm{let}\:\mathrm{A}_{\mathrm{ABCD}} \:=\:\mathrm{area}\:\mathrm{of}\:\mathrm{ABCD} \\ $$$$\mathrm{and}\:\mathrm{P}_{\mathrm{ABCD}}…
Question Number 144072 by bobhans last updated on 21/Jun/21 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{reduction}\:\mathrm{formula}\:\mathrm{to} \\ $$$$\mathrm{rewrite}\:−\mathrm{3}\:\mathrm{sin}\:\mathrm{x}\:−\mathrm{3}\:\mathrm{cos}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{form}\:\mathrm{K}\:\mathrm{sin}\:\left(\mathrm{x}+\alpha\right)\:. \\ $$ Answered by liberty last updated on 21/Jun/21 $$\mathrm{because}\:\begin{cases}{\mathrm{a}=−\mathrm{3}}\\{\mathrm{b}=−\mathrm{3}}\end{cases}\:\mathrm{we}\:\mathrm{have}\:\mathrm{K}=\sqrt{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}}…