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Question Number 90596 by I want to learn more last updated on 24/Apr/20

If   sin(28)  =  a    and   cos(32)  =  b  Find  (i)  cos(28)              (ii) cos(64)              (iii) sin(4)

$$\mathrm{If}\:\:\:\mathrm{sin}\left(\mathrm{28}\right)\:\:=\:\:\mathrm{a}\:\:\:\:\mathrm{and}\:\:\:\mathrm{cos}\left(\mathrm{32}\right)\:\:=\:\:\mathrm{b} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{i}\right)\:\:\mathrm{cos}\left(\mathrm{28}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{ii}\right)\:\mathrm{cos}\left(\mathrm{64}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{iii}\right)\:\mathrm{sin}\left(\mathrm{4}\right) \\ $$

Answered by mahdi last updated on 25/Apr/20

i)cos28=(√(1−sin^2 28))=(√(1−a^2 ))  ii)cos64=cos(32+32)=2cos^2 32−1=2b^2 −1  iii)sin4=sin(32−28)=sin32.cos28−sin28.cos32  =a(√(1−b^2 ))−b(√(1−b^2 ))

$$\left.\mathrm{i}\right)\mathrm{cos28}=\sqrt{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \mathrm{28}}=\sqrt{\mathrm{1}−\mathrm{a}^{\mathrm{2}} } \\ $$$$\left.\mathrm{ii}\right)\mathrm{cos64}=\mathrm{cos}\left(\mathrm{32}+\mathrm{32}\right)=\mathrm{2cos}^{\mathrm{2}} \mathrm{32}−\mathrm{1}=\mathrm{2b}^{\mathrm{2}} −\mathrm{1} \\ $$$$\left.\mathrm{iii}\right)\mathrm{sin4}=\mathrm{sin}\left(\mathrm{32}−\mathrm{28}\right)=\mathrm{sin32}.\mathrm{cos28}−\mathrm{sin28}.\mathrm{cos32} \\ $$$$=\mathrm{a}\sqrt{\mathrm{1}−\mathrm{b}^{\mathrm{2}} }−\mathrm{b}\sqrt{\mathrm{1}−\mathrm{b}^{\mathrm{2}} } \\ $$

Commented by I want to learn more last updated on 25/Apr/20

Thanks sir

$$\mathrm{Thanks}\:\mathrm{sir} \\ $$

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.

$${I}\:{think}\:{we}\:{should}\:{avoid}\:{answering} \\ $$$${such}\:{types}\:{of}\:{question},\:{which}\:{helps} \\ $$$${students}\:{to}\:{do}\:{their}\:{home}\:{work}. \\ $$$${It}\:{is}\:{misuse}\:{of}\:{this}\:{forum}. \\ $$

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