Question #3104b

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Answer 1 · 2016-06-07T20:30:37

C) $sin(x)/cos(x)+cos(x)/sin(x)=csc(x)sec(x)$

$sin(x)/cos(x)+cos(x)/sin(x)$

(Multiply by $sin(x)/sin(x)$ and $cos(x)/cos(x)$ to give terms a common denominator)

$= sin^2(x)/(sin(x)cos(x))+cos^2(x)/(sin(x)cos(x))$

$=(sin^2(x)+cos^2(x))/(sin(x)cos(x))$

(Apply the identity $sin^2(x)+cos^2(x)=1$ )

$=1/(sin(x)cos(x))$

$=1/sin(x)*1/cos(x)$

(Apply the definitions $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ )

$=csc(x)sec(x)$

$=sec(x)csc(x)$

Thus the answer is C.