Calculate E=sin(arcsin1/2)+sin{arccos [(sqrt3)/2]}.

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neela | High School Teacher | (Level 3) Valedictorian

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To find the value of E

E=sin(arcsin1/2)+sin{arc[cos(sqrt3/2)]},

There are two terms . We shall simplify term by term.

Firrst term sin(arcsin1/2) = x say, then by definition,

arcsin1/2 =arcsinx. by comparison, oviously x=1/2.

The second term:

We know that arccos X  = arcsin sqrt(1-X^2). Use this idea here.

sin arc(cos(sqrt3/2))=y say.

y =sin[sinarcssqrt(1-(sqrt3/2)^2)]=sqrt(1-3/4)=sqrt(1/4) =1/2

Therefore, y=1/2

Therefore,E=x+y=1/2+1/2=1.

Threfore, the value of E is 1.

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