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Maths-

General

Easy

Question

If $A plus B equals fraction numerator pi over denominator 3 end fraction$ and cos A + cos B = 1, then -

cos(A – B) = 1/3
| cos A – cos B | = $\sqrt{\frac{2}{3}}$
$c o s (A - B) = - \frac{1}{3}$
$c o s A - c o s B ∣ = \frac{1}{2 \sqrt{3}}$

The correct answer is: | cos A – cos B | = $square root of fraction numerator 2 over denominator 3 end fraction end root$

$table row cell c o s invisible function application A plus c o s invisible function application B equals 1 end cell row cell 2 c o s invisible function application fraction numerator A plus B over denominator 2 end fraction c o s invisible function application fraction numerator A minus B over denominator 2 end fraction equals 1 rightwards double arrow c o s invisible function application fraction numerator A minus B over denominator 2 end fraction equals fraction numerator 1 over denominator square root of 3 end fraction end cell row cell rightwards double arrow c o s invisible function application left parenthesis A minus B right parenthesis equals 2 c o s to the power of 2 end exponent invisible function application fraction numerator A minus B over denominator 2 end fraction minus 1 equals fraction numerator 2 over denominator 3 end fraction minus 1 equals negative fraction numerator 1 over denominator 3 end fraction end cell row cell vertical line c o s invisible function application A minus c o s invisible function application B vertical line equals open vertical bar 2 s i n invisible function application fraction numerator A plus B over denominator 2 end fraction s i n invisible function application fraction numerator B minus A over denominator 2 end fraction close vertical bar equals square root of fraction numerator 2 over denominator 3 end fraction end root end cell end table$

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