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Category: Trigonometry

Question-199723

Question Number 199723 by cortano12 last updated on 08/Nov/23 Answered by AST last updated on 08/Nov/23 $${Suppose}\:{ABCD}\:{is}\:{a}\:{square} \\ $$$${Through}\:{P},{let}\:{the}\:{line}\:{parallel}\:{to}\:{BC}\:{meet}\:{AB} \\ $$$${at}\:{F};{then}\:{PF}=\mathrm{8}\Rightarrow\frac{{sin}\left(\mathrm{2}\alpha\right)}{\mathrm{1}}=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\Rightarrow{cos}\left(\mathrm{2}\alpha\right)=\frac{\mathrm{3}}{\mathrm{5}}=\frac{{AF}}{\mathrm{10}}\Rightarrow{AF}=\mathrm{6}\Rightarrow{PC}=\mathrm{2} \\ $$…

cos-x-cos-y-1-2-sin-x-sin-y-1-4-sin-2x-sin-2y-27-20-sin-x-y-

Question Number 199718 by cortano12 last updated on 08/Nov/23 $$\:\begin{cases}{\mathrm{cos}\:\mathrm{x}+\mathrm{cos}\:\mathrm{y}=\frac{\mathrm{1}}{\mathrm{2}}}\\{\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:\mathrm{y}=\frac{\mathrm{1}}{\mathrm{4}}}\\{\mathrm{sin}\:\mathrm{2x}\:+\:\mathrm{sin}\:\mathrm{2y}=−\frac{\mathrm{27}}{\mathrm{20}}}\end{cases} \\ $$$$\:\:\:\mathrm{sin}\:\left(\mathrm{x}+\mathrm{y}\right)\:=\:… \\ $$ Answered by Sutrisno last updated on 08/Nov/23 $$\left({cosx}+{cosy}\right)\left({sinx}+{siny}\right)=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$${cosxsinx}+{cosxsiny}+{cosysinx}+{cosysiny}=\frac{\mathrm{1}}{\mathrm{8}} \\…

Question-199480

Question Number 199480 by Abdullahrussell last updated on 04/Nov/23 Commented by mr W last updated on 04/Nov/23 $$=\frac{\mathrm{sin}\:\theta+\mathrm{sin}\:\mathrm{50}°+\mathrm{1}+\mathrm{sin}\:\mathrm{50}°}{\mathrm{cos}\:\theta+\mathrm{cos}\:\mathrm{50}°+\mathrm{0}−\mathrm{cos}\:\mathrm{50}°} \\ $$$$=\frac{\mathrm{sin}\:\theta+\mathrm{1}+\mathrm{2}\:\mathrm{sin}\:\mathrm{50}°}{\mathrm{cos}\:\theta} \\ $$ Terms of Service…

x-

Question Number 199424 by cortano12 last updated on 03/Nov/23 $$\:\:\:\boldsymbol{{x}} \\ $$ Answered by Frix last updated on 04/Nov/23 $${f}\left({x}\right)=\frac{\mathrm{cos}\:{x}}{\mathrm{3}}\left(\mathrm{6sin}^{\mathrm{3}} \:{x}\:−\mathrm{4sin}^{\mathrm{2}} \:{x}\:+\mathrm{1}\right) \\ $$$${f}'\left({x}\right)=−\mathrm{sin}\:{x}\:\left(\mathrm{1}−\mathrm{2sin}\:{x}\right)\left(\mathrm{3}−\mathrm{4sin}^{\mathrm{2}} \:{x}\right)…