Question

Simplifica : (Sec2x + csc2x/tanx+cotx) - tanx

Answer 1

Respuesta:

Simplifica : (Sec2x + csc2x/tanx+cotx) - tanx

Explicación paso a paso:

$\left(\frac{sec^2x+csc^2x}{tanx+cotx}\right)-tanx\\\\=\frac{\sec ^2\left(x\right)+\csc ^2\left(x\right)}{\tan \left(x\right)+\cot \left(x\right)}-\tan \left(x\right)\\\\=\frac{\sec ^2\left(x\right)+\csc ^2\left(x\right)}{\tan \left(x\right)+\cot \left(x\right)}-\frac{\tan \left(x\right)\left(\tan \left(x\right)+\cot \left(x\right)\right)}{\tan \left(x\right)+\cot \left(x\right)}$

$=\frac{\sec ^2\left(x\right)+\csc ^2\left(x\right)-\tan \left(x\right)\left(\tan \left(x\right)+\cot \left(x\right)\right)}{\tan \left(x\right)+\cot \left(x\right)}\\\\=\frac{\sec ^2\left(x\right)+\csc ^2\left(x\right)-\sec ^2\left(x\right)}{\tan \left(x\right)+\cot \left(x\right)}$

$=\frac{\csc ^2\left(x\right)}{\tan \left(x\right)+\cot \left(x\right)}\\\\=\frac{\cos \left(x\right)}{\left(\cos ^2\left(x\right)+\sin ^2\left(x\right)\right)\sin \left(x\right)}\\\\=\cot \left(x\right)$