Question Number 90596 by I want to learn more last updated on 24/Apr/20
$$\mathrm{If}\:\:\:\mathrm{sin}\left(\mathrm{28}\right)\:\:=\:\:\mathrm{a}\:\:\:\:\mathrm{and}\:\:\:\mathrm{cos}\left(\mathrm{32}\right)\:\:=\:\:\mathrm{b} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{i}\right)\:\:\mathrm{cos}\left(\mathrm{28}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{ii}\right)\:\mathrm{cos}\left(\mathrm{64}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{iii}\right)\:\mathrm{sin}\left(\mathrm{4}\right) \\ $$
Answered by mahdi last updated on 25/Apr/20
$$\left.\mathrm{i}\right)\mathrm{cos28}=\sqrt{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \mathrm{28}}=\sqrt{\mathrm{1}−\mathrm{a}^{\mathrm{2}} } \\ $$$$\left.\mathrm{ii}\right)\mathrm{cos64}=\mathrm{cos}\left(\mathrm{32}+\mathrm{32}\right)=\mathrm{2cos}^{\mathrm{2}} \mathrm{32}−\mathrm{1}=\mathrm{2b}^{\mathrm{2}} −\mathrm{1} \\ $$$$\left.\mathrm{iii}\right)\mathrm{sin4}=\mathrm{sin}\left(\mathrm{32}−\mathrm{28}\right)=\mathrm{sin32}.\mathrm{cos28}−\mathrm{sin28}.\mathrm{cos32} \\ $$$$=\mathrm{a}\sqrt{\mathrm{1}−\mathrm{b}^{\mathrm{2}} }−\mathrm{b}\sqrt{\mathrm{1}−\mathrm{b}^{\mathrm{2}} } \\ $$
Commented by I want to learn more last updated on 25/Apr/20
$$\mathrm{Thanks}\:\mathrm{sir} \\ $$
Commented by $@ty@m123 last updated on 25/Apr/20
$${I}\:{think}\:{we}\:{should}\:{avoid}\:{answering} \\ $$$${such}\:{types}\:{of}\:{question},\:{which}\:{helps} \\ $$$${students}\:{to}\:{do}\:{their}\:{home}\:{work}. \\ $$$${It}\:{is}\:{misuse}\:{of}\:{this}\:{forum}. \\ $$