Question

Multiply and simplify:$\frac{(1+\tan (\theta \left)\right)(1+\tan (\theta \left)\right)-sec\left(\theta \right)}{\tan \left(\theta \right)}$

Short answer

on simplifying we get$2.$

Step-by-step solution

Given information

We are given an expression$\frac{(1+\tan (\theta \left)\right)(1+\tan (\theta \left)\right)-sec\left(\theta \right)}{\tan \left(\theta \right)}$

Multiply and simplify

We get,

$$\begin{gathered} \frac{(1+\tan (\theta \left)\right)(1+\tan (\theta \left)\right)-sec\left(\theta \right)}{\tan \left(\theta \right)} \\ =\frac{1+2\tan \left(\theta \right)+{\tan }^2\left(\theta \right)-se{c}^2\left(\theta \right)}{\tan \left(\theta \right)} \\ =\frac{se{c}^2\left(\theta \right)+2\tan \left(\theta \right)-se{c}^2\left(\theta \right)}{\tan \left(\theta \right)} \\ =\frac{2\tan \left(\theta \right)}{\tan \left(\theta \right)} \\ =2 \end{gathered}$$

Conclusion

On simplifying we get the expression as$2.$