Question

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

Short answer

On simplifying we get the answer as$2$

Step-by-step solution

Given information

We are given an equation$\frac{\left(\sin \right(\theta )+\cos (\theta \left)\right)\left(\sin \right(\theta )+\cos (\theta \left)\right)-1}{\sin \left(\theta \right)\cos \left(\theta \right)}$

Multiply and simplify

We get,

$$\begin{gathered} \frac{\left(\sin \right(\theta )+\cos (\theta \left)\right)\left(\sin \right(\theta )+\cos (\theta \left)\right)-1}{\sin \left(\theta \right)\cos \left(\theta \right)} \\ =\frac{{\sin }^2\left(\theta \right)+{\cos }^2\left(\theta \right)+2\sin \left(\theta \right)\cos \left(\theta \right)-1}{\sin \left(\theta \right)\cos \left(\theta \right)} \\ =\frac{1+2\sin \left(\theta \right)\cos \left(\theta \right)-1}{\sin \left(\theta \right)\cos \left(\theta \right)} \\ =\frac{2\sin \left(\theta \right)\cos \left(\theta \right)}{\sin \left(\theta \right)\cos \left(\theta \right)} \\ =2 \end{gathered}$$

Conclusion

on simplifying we get 2.