If $secθ space equals space 25 over 7 comma$ then the values of tan θ is

$7 over 24$
$27 over 7$
$24 over 7$
$22 over 7$

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Solution

24 over 7

Tips: -

secθ space equals space OP over OQ equals 25 over 7 comma space space space sec squared straight theta space equals space 1 plus tan squared straight theta rightwards double arrow space space space space open parentheses 25 over 7 close parentheses squared minus 1 space equals space tan squared straight theta space equals space fraction numerator 625 minus 49 over denominator 49 end fraction equals tan squared straight theta rightwards double arrow space space tan space straight theta space equals space square root of 576 over 49 end root space equals space 24 over 7 space space space Ans. space left parenthesis straight c right parenthesis

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