Question #3d30a

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Answer 1 · 2017-06-24T18:59:49

Multiply both sides by $sin(x)cos(x)$ .

Here is how you can prove the identity is true. First, express all terms as either $sin(x)$ or $cos(x)$

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

Then multiply both sides by $sin(x)cos(x)$

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

The left hand side multiplies $sin(x)cos(x)$ through the numerator, giving

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

The right hand side multiplies $sin(x)cos(x)$ though each term, giving

$=cos^2(x)+sin^2(x)=1$

Because the left hand side equals the right hand side, the identity is proven.