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Maths-

General

Easy

Question

If $y equals left parenthesis 1 plus tan space A right parenthesis left parenthesis 1 minus tan space B right parenthesis$ where $A minus B equals pi over 4$ then $left parenthesis y plus 1 right parenthesis to the power of y plus 1 end exponent$ =

27
9
81
4

hint Hint:

Apply tangent on both sides of the angle equation to solve the question.

The correct answer is: 27

$G i v e n comma y equals left parenthesis 1 plus tan space A right parenthesis left parenthesis 1 minus tan space B right parenthesis A minus B equals pi over 4 T o space f i n d comma left parenthesis y plus 1 right parenthesis to the power of y plus 1 end exponent N o w comma A minus B equals pi over 4 A equals pi over 4 plus B A p p l y i g n space tan g e n t space o n space b o t h space t h e space s i d e s comma tan A equals tan open parentheses pi over 4 plus B close parentheses U sin g space f o r m u l a space tan open parentheses A plus B close parentheses equals fraction numerator tan begin display style A end style plus tan B over denominator 1 minus tan begin display style A end style tan B end fraction comma tan A equals fraction numerator tan begin display style straight pi over 4 end style plus tan B over denominator 1 minus tan begin display style straight pi over 4 end style tan B end fraction tan A equals fraction numerator 1 plus tan B over denominator 1 minus tan B end fraction U sin g space C o m p o n e n d o comma tan A plus 1 equals fraction numerator 1 plus tan B plus 1 minus tan B over denominator 1 minus tan B end fraction tan A plus 1 equals fraction numerator 2 over denominator 1 minus tan B end fraction open parentheses 1 plus tan A close parentheses open parentheses 1 minus tan B close parentheses equals 2 equals y therefore left parenthesis y plus 1 right parenthesis to the power of y plus 1 end exponent equals left parenthesis 2 plus 1 right parenthesis to the power of 2 plus 1 end exponent equals 3 cubed equals 27$

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