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Question

If $tan invisible function application open parentheses A minus B close parentheses equals 1$ and $sec invisible function application open parentheses A plus B close parentheses equals 2 divided by square root of 3 comma blank$ then the smallest positive values of $A blank$ and $B comma$ respectively, are

$\frac{25 π}{24}, \frac{19 π}{24}$
$\frac{19 π}{24}, \frac{25 π}{24}$
$\frac{31 π}{24}, \frac{13 π}{24}$
$\frac{13 π}{24}, \frac{31 π}{24}$

The correct answer is: $fraction numerator 25 pi over denominator 24 end fraction comma fraction numerator 19 pi over denominator 24 end fraction$

$tan invisible function application open parentheses A minus B close parentheses equals 1$
$rightwards double arrow A minus B equals n subscript 1 end subscript pi plus fraction numerator pi over denominator 4 end fraction equals fraction numerator pi over denominator 4 end fraction comma fraction numerator 3 pi over denominator 4 end fraction comma negative fraction numerator 3 pi over denominator 4 end fraction comma horizontal ellipsis$
$sec invisible function application open parentheses A plus B close parentheses equals fraction numerator 2 over denominator square root of 5 end fraction blank rightwards double arrow A plus B equals 2 n subscript 2 end subscript pi plus-or-minus fraction numerator pi over denominator 6 end fraction equals fraction numerator pi over denominator 6 end fraction comma fraction numerator 11 pi over denominator 6 end fraction comma horizontal ellipsis$
For the least positive values of $A$ and $blank B comma$
$A plus B equals fraction numerator 11 pi over denominator 6 end fraction comma blank A minus B equals fraction numerator pi over denominator 4 end fraction blank rightwards double arrow B equals fraction numerator 19 pi over denominator 24 end fraction comma A equals fraction numerator 25 pi over denominator 24 end fraction$

Related Questions to study

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