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Category: Trigonometry

The-solution-of-the-equation-cos-2-2cos-4sin-sin2-where-0-pi-is-

Question Number 17151 by Tinkutara last updated on 01/Jul/17 $$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{cos}^{\mathrm{2}} \theta\:−\:\mathrm{2cos}\theta\:=\:\mathrm{4sin}\theta\:−\:\mathrm{sin2}\theta\:\mathrm{where} \\ $$$$\theta\:\in\:\left[\mathrm{0},\:\pi\right]\:\mathrm{is} \\ $$ Answered by ajfour last updated on 01/Jul/17 $$\mathrm{4sin}\:\theta−\mathrm{2sin}\:\theta\mathrm{cos}\:\theta+\mathrm{2cos}\:\theta−\mathrm{cos}\:^{\mathrm{2}}…

The-number-of-solutions-of-the-equation-cos-pi-x-4-cos-pi-x-1-is-

Question Number 17148 by Tinkutara last updated on 01/Jul/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{cos}\:\left(\pi\sqrt{{x}\:−\:\mathrm{4}}\right)\:\mathrm{cos}\:\left(\pi\sqrt{{x}}\right)\:=\:\mathrm{1}\:\mathrm{is} \\ $$ Answered by ajfour last updated on 01/Jul/17 $$\Rightarrow\:\:\:\mathrm{cos}\:\left(\pi\sqrt{\mathrm{x}−\mathrm{4}}\right)=\pm\mathrm{1} \\ $$$$\mathrm{and}\:\:\:\mathrm{cos}\:\left(\pi\sqrt{\mathrm{x}}\right)=\pm\mathrm{1} \\…

Question-17119

Question Number 17119 by gourav~ last updated on 01/Jul/17 Commented by prakash jain last updated on 01/Jul/17 $$\frac{\mathrm{sin}\:\left({A}+\mathrm{3}{B}\right)+\mathrm{sin}\:\left(\mathrm{3}{A}+{B}\right)}{\mathrm{sin}\:\mathrm{2}{A}+\mathrm{sin}\:\mathrm{2}{B}} \\ $$$$=\frac{\mathrm{2sin}\:\left(\frac{\mathrm{4}{A}+\mathrm{4}{B}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{\mathrm{2}{B}−\mathrm{2}{A}}{\mathrm{2}}\right)}{\mathrm{2sin}\:\left({A}+{B}\right)\mathrm{cos}\:\left({A}−{B}\right)} \\ $$$$=\frac{\mathrm{2sin}\:\left(\mathrm{2}\left({A}+{B}\right)\right)\mathrm{cos}\:\left({A}−{B}\right)}{\mathrm{2sin}\:\left({A}+{B}\right)\mathrm{cos}\:\left({A}−{B}\right)} \\ $$$$=\frac{\mathrm{sin}\:\left(\mathrm{2}\left({A}+{B}\right)\right)}{\mathrm{sin}\:\left({A}+{B}\right)} \\…

The-total-number-of-solutions-of-the-equation-tan-x-sec-x-2-which-lie-in-the-interval-0-2pi-is-

Question Number 17095 by Tinkutara last updated on 30/Jun/17 $$\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{tan}\:{x}\:+\:\mathrm{sec}\:{x}\:=\:\mathrm{2}\:\mathrm{which}\:\mathrm{lie}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{interval}\:\left[\mathrm{0},\:\mathrm{2}\pi\right]\:\mathrm{is} \\ $$ Answered by sma3l2996 last updated on 30/Jun/17 $${tanx}+{secx}=\mathrm{2}\Leftrightarrow{tanx}+\sqrt{\mathrm{1}+{tan}^{\mathrm{2}} {x}}=\mathrm{2}…

The-total-number-of-solutions-of-the-equation-tan-3x-tan-2x-tan-3x-tan-2x-1-in-0-2pi-is-

Question Number 17096 by Tinkutara last updated on 30/Jun/17 $$\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation} \\ $$$$\mathrm{tan}\:\mathrm{3}{x}\:−\:\mathrm{tan}\:\mathrm{2}{x}\:−\:\mathrm{tan}\:\mathrm{3}{x}\:\mathrm{tan}\:\mathrm{2}{x}\:=\:\mathrm{1}\:\mathrm{in} \\ $$$$\left[\mathrm{0},\:\mathrm{2}\pi\right]\:\mathrm{is} \\ $$ Answered by sma3l2996 last updated on 30/Jun/17…

sin-4-2-cos-4-2-1-2-

Question Number 17080 by Kunal kumar shukla last updated on 30/Jun/17 $$\mathrm{sin}^{\mathrm{4}} \theta/\mathrm{2}+\mathrm{cos}\:^{\mathrm{4}} \theta/\mathrm{2}\geqslant\mathrm{1}/\mathrm{2} \\ $$ Answered by virus last updated on 30/Jun/17 $$\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \left(\theta/\mathrm{2}\right)\mathrm{cos}\:^{\mathrm{2}}…