Question Number 84019 by mathocean1 last updated on 08/Mar/20
$${Show}\:{that}: \\ $$$$\mathrm{1}\bullet\:\:\:{tan}\mathrm{3}{x}=\frac{\mathrm{3}−{tan}^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{3}{tan}^{\mathrm{2}} {x}} \\ $$$${using}\:{cos}\mathrm{3}{x}=\mathrm{4}{cos}^{\mathrm{4}} {x}−\mathrm{3}{cosx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{sin}\mathrm{3}{x}=−\mathrm{4}{sin}^{\mathrm{3}} {x}+\mathrm{3}{sinx} \\ $$$${Thanks}… \\ $$
Commented by MJS last updated on 08/Mar/20
$$\mathrm{it}'\mathrm{s}\:\mathrm{wrong}: \\ $$$$\mathrm{tan}\:\mathrm{3}{x}\:=−\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}×\frac{\mathrm{1}−\mathrm{4cos}^{\mathrm{2}} \:{x}}{\mathrm{1}−\mathrm{4sin}^{\mathrm{2}} \:{x}} \\ $$$$\frac{\mathrm{3}−\mathrm{tan}^{\mathrm{2}} \:{x}}{\mathrm{1}−\mathrm{3tan}^{\mathrm{2}} \:{x}}=\frac{\mathrm{1}−\mathrm{4cos}^{\mathrm{2}} \:{x}}{\mathrm{1}−\mathrm{4sin}^{\mathrm{2}} \:{x}} \\ $$
Commented by $@ty@m123 last updated on 08/Mar/20
$${There}\:{is}\:{a}\:{typo}\:{in}\:{question} \\ $$$${It}\:{is}\:\:\:\:\:\mathrm{tan}\:\mathrm{3}{x}=\frac{\left(\mathrm{3}−\mathrm{tan}^{\mathrm{2}} \:{x}\right)\mathrm{tan}\:{x}}{\mathrm{1}−\mathrm{3tan}^{\mathrm{2}} \:{x}} \\ $$
Answered by Rio Michael last updated on 08/Mar/20
$$\left.{b}\right)\:\mathrm{cos}\:\mathrm{3}{x}\:=\:\mathrm{cos}\:\left(\mathrm{2}{x}\:+\:{x}\right)\:=\:\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:{x}\:−\:\mathrm{sin}\:\mathrm{2}{x}\:\mathrm{sin}\:{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left(\mathrm{2cos}\:^{\mathrm{2}} {x}\:−\mathrm{1}\right)\mathrm{cos}\:{x}\:−\:\mathrm{2sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:{x}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{2cos}\:^{\mathrm{3}} {x}−\mathrm{cos}\:{x}\:−\mathrm{2}\:\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}\right)\mathrm{cos}\:{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{2cos}\:^{\mathrm{3}} {x}−\mathrm{cos}\:{x}\:−\mathrm{2cos}\:{x}\:+\mathrm{2cos}\:^{\mathrm{3}} {x}\:=\:\mathrm{4cos}\:^{\mathrm{3}} {x}−\mathrm{3cos}\:{x} \\ $$
Commented by mathocean1 last updated on 08/Mar/20
$${please}\:{sir}\:{we}\:{want}\:{to}\:{show}\:\mathrm{1}\bullet\: \\ $$
Answered by $@ty@m123 last updated on 08/Mar/20
$${See}\:{Q}.\:{No}.\:\mathrm{76497} \\ $$