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Some Applications Of Trigonometry

Question

The value of $fraction numerator 5 space sin squared 30 degree plus cos squared 45 degree plus 4 space tan squared space 60 degree over denominator 2 space sin space 30 degree space cos space 60 degree space plus space tan space 45 degree end fraction$ is

$9 1 over 6$
$8 1 fifth$
$5 2 over 6$
$4 1 over 6$

Solution

9 1 over 6