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Doctors Medicines MCQs Q&A

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Recall the formula for $cos(alpha+beta)$:
$cos(alpha+beta)=cos(alpha)*cos(beta)-sin(alpha)*sin(beta)$

Using this formula for $alpha=7pi/6$ and $beta=-pi/2$, we get:

$cos(7pi/6)*cos(-pi/2)-sin(7pi/6)*sin(-pi/2)=$
$=cos(7pi/6+(-pi/2))=$
$=cos((7pi)/6-(3pi)/6)=$
$=cos((2pi)/3)=-cos(pi-(2pi)/3)=-cos(pi/3)=-1/2$

As a check, notice that
$cos(7pi/6)=-cos(pi/6)=-sqrt(3)/2$,
$cos(-pi/2)=0$,
$sin(7pi/6)=-sin(pi/6)=-1/2$,
$sin(-pi/2)=-1$.
Performing direct calculations, we get the same $-1/2$.
Check!

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