How do you prove $cos(x)tan(X) + sin(x)cot(x) = sin(x) + cos^2(x)$ ?

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Answer 1 · 2015-12-20T06:39:32

Cannot be proven.

Know that: ${(tan(x)=sin(x)/cos(x)),(cot(x)=cos(x)/sin(x)):}$

Thus,

$cos(x)tan(x)+sin(x)cot(x)$

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

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

Thus, the identity is invalid and cannot be proven.

How do you prove cos(x)tan(X) + sin(x)cot(x) = sin(x) + cos^2(x)cos(x)tan(X) + sin(x)cot(x) = sin(x) + cos^2(x)?