Question

Urgente alguien me puede ayudar es para hoy

Answer 1

Respuesta:

$\frac{\tan \left(x\right)\left(1+\cot \left(x\right)\right)-1}{\sec \left(x\right)\left(1+\cos \left(x\right)\right)+1}\\\\\sec \left(x\right)\left(1+\cos \left(x\right)\right)\\\\\mathrm{Usar\:la\:siguiente\:identidad}:\quad \cos \left(x\right)=\frac{1}{\sec \left(x\right)}\\\\=\left(1+\frac{1}{\sec \left(x\right)}\right)\sec \left(x\right)=\sec \left(x\right)\left(1+\frac{1}{\sec \left(x\right)}\right)$

$\mathrm{Poner\:los\:parentesis\:utilizando}:\quad \:a\left(b+c\right)=ab+ac\\a=\sec \left(x\right),\:b=1,\:c=\frac{1}{\sec \left(x\right)}\\\\=\sec \left(x\right)\cdot \:1+\sec \left(x\right)\frac{1}{\sec \left(x\right)}\\\\=1\cdot \sec \left(x\right)+\frac{1}{\sec \left(x\right)}\sec \left(x\right)$

$\frac{1}{\sec \left(x\right)}\sec \left(x\right)\\\\=\frac{\sec \left(x\right)}{\sec \left(x\right)}\\\\=1\\\\=\sec \left(x\right)+1\\\\=\frac{\tan \left(x\right)\left(\cot \left(x\right)+1\right)-1}{1+\sec \left(x\right)+1}$

$1+\sec \left(x\right)+1=\sec \left(x\right)+1+1=\sec \left(x\right)+2\\\\=\frac{\tan \left(x\right)\left(\cot \left(x\right)+1\right)-1}{\sec \left(x\right)+2}$