Question

Sendo tgx=3, calcule o valor de y= tgx+cotgx
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cossec²x

Answer 1

$\frac{tanx+cotx}{csc^2x}=\frac{\frac{sinx}{cosx}+\frac{cosx}{sinx}}{\frac{1}{sin^2x}}=\frac{\frac{sin^2x+cos^2x}{sinxcosx}}{\frac{1}{sin^2x}}=\frac{\frac{1}{sinxcosx}}{\frac{1}{sin^2x}}=\frac{1}{sinxcosx}*sin^2x=$
$\frac{sinx}{cosx}=tanx=\boxed{3}$