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$I f tan invisible function application fraction numerator pi over denominator 9 end fraction comma blank x blank a n d tan invisible function application fraction numerator 5 pi over denominator 18 end fraction$ are in A.P. and $tan invisible function application fraction numerator pi over denominator 9 end fraction comma blank y blank a n d tan invisible function application fraction numerator 7 pi over denominator 18 end fraction$ are also in A.P., then

$2 x = y$
$x > 2$
$x = y$
None of these

The correct answer is: $2 x equals y$

By the given conditions $tan invisible function application fraction numerator pi over denominator 9 end fraction plus tan invisible function application fraction numerator 5 pi over denominator 18 end fraction equals 2 x.$
$tan invisible function application fraction numerator pi over denominator 9 end fraction plus tan invisible function application fraction numerator 7 pi over denominator 18 end fraction equals 2 y blank$
$rightwards double arrow 2 x equals tan invisible function application 20 degree plus tan invisible function application 50 degree$
$equals fraction numerator sin invisible function application 20 degree over denominator cos invisible function application 20 degree end fraction plus fraction numerator sin invisible function application 50 degree over denominator cos invisible function application 50 degree end fraction$
$equals fraction numerator sin invisible function application 20 degree blank cos invisible function application 50 degree plus cos invisible function application 20 degree blank sin invisible function application 50 degree over denominator cos invisible function application 20 degree blank cos invisible function application 50 degree end fraction$
$equals fraction numerator sin invisible function application 70 degree over denominator cos invisible function application 20 degree blank cos invisible function application 50 degree end fraction$
$equals fraction numerator cos invisible function application 20 degree over denominator cos invisible function application 20 degree blank cos invisible function application 50 degree end fraction equals fraction numerator 1 over denominator cos invisible function application 50 degree end fraction equals fraction numerator 1 over denominator sin invisible function application 40 degree end fraction equals c o s e c blank 40 degree$
$2 y equals blank tan invisible function application 20 degree plus tan invisible function application 70 degree$
$equals fraction numerator sin invisible function application 20 degree over denominator cos invisible function application 20 degree end fraction plus fraction numerator sin invisible function application 70 degree over denominator cos invisible function application 70 degree end fraction$
$equals fraction numerator sin invisible function application 90 degree over denominator cos invisible function application 20 degree blank cos invisible function application 70 degree end fraction$
$equals fraction numerator 1 over denominator cos invisible function application 20 degree cos invisible function application 70 degree end fraction equals fraction numerator 1 over denominator cos invisible function application 20 degree sin invisible function application 20 degree end fraction$
$equals fraction numerator 2 over denominator 2 sin invisible function application 20 degree cos invisible function application 20 degree end fraction equals fraction numerator 2 over denominator sin invisible function application 40 degree end fraction equals 2 blank c o s e c blank 40 degree$
$therefore 2 y equals 2 open parentheses 2 x close parentheses rightwards double arrow y equals 2 x$

Related Questions to study

Sum of all the solutions in $open square brackets 0 comma blank 4 pi close square brackets$ of the equation $tan invisible function application x plus cot invisible function application x plus 1 equals cos invisible function application open parentheses x plus fraction numerator pi over denominator 4 end fraction close parentheses$ is

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If $S equals open curly brackets x element of N blank colon 2 plus log subscript 2 end subscript invisible function application square root of x plus 1 end root greater than 1 minus log subscript 1 divided by 2 end subscript invisible function application square root of 4 minus x to the power of 2 end exponent end root close curly brackets comma$ then

$log subscript 4 end subscript invisible function application 18$ is

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parallel

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parallel

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