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Question

If $y equals open parentheses 1 plus tan invisible function application A close parentheses open parentheses 1 minus tan invisible function application B close parentheses blank$ where $blank A minus B equals fraction numerator pi over denominator 4 end fraction comma$ then $open parentheses y plus 1 close parentheses to the power of y plus 1 end exponent blank$ is equal to

9
4
27
81

The correct answer is: 27

$A minus B equals fraction numerator pi over denominator 4 end fraction rightwards double arrow tan invisible function application open parentheses A minus B close parentheses equals tan invisible function application fraction numerator pi over denominator 4 end fraction$
$rightwards double arrow fraction numerator tan invisible function application A minus tan invisible function application B over denominator 1 plus tan invisible function application A tan invisible function application B end fraction$
$rightwards double arrow tan invisible function application A minus tan invisible function application B minus tan invisible function application A tan invisible function application B equals 1$
$rightwards double arrow tan invisible function application A minus tan invisible function application B minus tan invisible function application A tan invisible function application B plus 1 equals 2$
$rightwards double arrow open parentheses 1 plus tan invisible function application A close parentheses open parentheses 1 minus tan invisible function application B close parentheses equals 2 rightwards double arrow y equals 2$
$H e n c e comma blank open parentheses y plus 1 close parentheses to the power of y plus 1 end exponent equals open parentheses 2 plus 1 close parentheses to the power of 2 plus 1 end exponent equals open parentheses 3 close parentheses to the power of 3 end exponent equals 27$

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