Question Number 182552 by Acem last updated on 11/Dec/22 $${Find}\:{the}\:{period}\:{of}\:{the}\:{following}: \\ $$$$\:{a}\bullet\:\mathrm{sin}\:\mathrm{4}{x}\:\mathrm{sin}\:\mathrm{3}{x} \\ $$$$\:{b}\bullet\:\mathrm{sin}\:\pi{x}+\:\mathrm{cos}\:{x} \\ $$$$\:{c}\bullet\:\frac{\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{3}{x}−\:\mathrm{3}\:\mathrm{tan}\:\mathrm{4}{x}+\:\mathrm{4}\:\mathrm{cot}\:\mathrm{6}{x}}{\mid\mathrm{cosec}\:\mathrm{8}{x}\mid−\:\mathrm{sec}^{\mathrm{3}} \:\mathrm{10}{x}+\:\sqrt{\mathrm{cot}\:\mathrm{12}{x}}} \\ $$ Terms of Service Privacy Policy…
Question Number 116966 by bobhans last updated on 08/Oct/20 $$\mathrm{4}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{5}}\right)−\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{239}}\right)\:=\:? \\ $$ Answered by bemath last updated on 08/Oct/20 Answered by TANMAY PANACEA…
Question Number 116964 by saorey0202 last updated on 08/Oct/20 Answered by Bird last updated on 08/Oct/20 $${we}\:{have}\:\mathrm{1}+{ix}\:=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:{e}^{{iarctan}\left({x}\right)} \\ $$$$\mathrm{1}−{ix}\:=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:{e}^{−{i}\:{arctan}\left({x}\right)} \:\Rightarrow \\ $$$$\frac{\mathrm{1}+{ix}}{\mathrm{1}−{ix}}\:={e}^{\mathrm{2}{i}\:{arctan}\left({x}\right)} \\…
Question Number 51367 by rahul 19 last updated on 26/Dec/18 $${Evaluate}: \\ $$$$\mathrm{cot}^{−\mathrm{1}} \left[\frac{\sqrt{\mathrm{1}−\mathrm{sin}{x}}+\sqrt{\mathrm{1}+\mathrm{sin}{x}}}{\:\sqrt{\mathrm{1}−\mathrm{sin}{x}}−\sqrt{\mathrm{1}+\mathrm{sin}{x}}}\right]\:=\:? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 26/Dec/18 $${case}−\mathrm{1}\:\:{a}>{b} \\…
Question Number 51364 by rahul 19 last updated on 26/Dec/18 $${The}\:{value}\:{of}\:{x}\:{for}\:{which} \\ $$$$\mathrm{sin}\left(\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{1}+{x}\right)\right)=\mathrm{cos}\left(\mathrm{tan}^{−\mathrm{1}} {x}\right)\:{is}\:? \\ $$ Commented by rahul 19 last updated on 26/Dec/18…
Question Number 116891 by bemath last updated on 07/Oct/20 $$\mathrm{Proof}\:\mathrm{that}\:\frac{\mathrm{4}\left(\mathrm{cos}\:^{\mathrm{4}} \left({a}\right)+\mathrm{sin}\:^{\mathrm{4}} \left({a}\right)\right)}{\mathrm{cos}\:^{\mathrm{4}} \left({a}\right)−\mathrm{sin}\:^{\mathrm{4}} \left({a}\right)}\:=\:\left(\mathrm{3}+\mathrm{cos}\:\left(\mathrm{4}{a}\right)\right)\mathrm{sec}\:\left(\mathrm{2}{a}\right)\: \\ $$ Answered by john santu last updated on 07/Oct/20 $$\Rightarrow\:\frac{\mathrm{4}\left\{\left(\mathrm{sin}\:^{\mathrm{2}}…
Question Number 51356 by rahul 19 last updated on 26/Dec/18 $${Evaluate}\:: \\ $$$$\mathrm{tan}\:\left\{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \frac{\sqrt{\mathrm{5}}}{\mathrm{3}}\right\}\:? \\ $$ Commented by rahul 19 last updated on 26/Dec/18 $${Ans}\rightarrow\:\frac{\mathrm{3}−\sqrt{\mathrm{5}}}{\mathrm{2}}.…
Question Number 116832 by bemath last updated on 07/Oct/20 $$\mathrm{If}\:\mathrm{19}\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{37}\:\mathrm{cos}\:\mathrm{2x}+\mathrm{38}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x} \\ $$$$\mathrm{then}\:\mathrm{tan}\:\mathrm{x}\:=\:\_\_ \\ $$ Answered by bobhans last updated on 07/Oct/20 $$\Rightarrow\mathrm{19}\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{37}\:\mathrm{cos}\:\mathrm{2x}+\mathrm{38sin}\:^{\mathrm{2}} \mathrm{x} \\…
Question Number 182332 by mnjuly1970 last updated on 07/Dec/22 $$ \\ $$$$\mathrm{If}\:\:,\:\:\:{f}\:\left({x}\right)\:=\:\mathrm{2}{cos}^{\:\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)\:−\lfloor\:\frac{\mathrm{1}}{\mathrm{3}}\:+{cos}\left({x}\right)\:\rfloor \\ $$$$\:\:{then}\:{find}\:{the}\:{range}\:{of}\::\:\:\:{R}_{\:{f}} \\ $$ Answered by floor(10²Eta[1]) last updated on 07/Dec/22 $$−\mathrm{1}\leqslant\mathrm{cosx}\leqslant\mathrm{1}\Rightarrow\frac{−\mathrm{2}}{\mathrm{3}}\leqslant\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{cosx}\leqslant\frac{\mathrm{4}}{\mathrm{3}}…
Question Number 116768 by bemath last updated on 06/Oct/20 $$\mathrm{sin}\:\left(\mathrm{4sin}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)\:=\:\mathrm{sin}\:\left(\mathrm{2sin}^{−\mathrm{1}} \left(\mathrm{x}\right)\right) \\ $$ Answered by bobhans last updated on 06/Oct/20 $$\mathrm{letting}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=\:\mathrm{z}\Rightarrow\mathrm{sin}\:\mathrm{z}\:=\:\mathrm{x} \\ $$$$\Rightarrow\:\mathrm{sin}\:\left(\mathrm{4z}\right)\:=\:\mathrm{sin}\:\left(\mathrm{2z}\right)\:…