Question

Help me simplify I don’t understand homework and I have to show work .

Answer 1

The Solution:

Given the expression below:

`(\left(sin\theta+cos\theta\right)^2)/(1+2sin\theta\:cos\theta)`

We are required to simplify the above expression.

`\begin{gathered} (\sin \theta+\cos \theta)^2=\sin ^2\theta+2\sin \theta\cos \theta+\cos ^2\theta=\sin ^2\theta+\cos ^2\theta+2\sin \theta\cos \theta \\ =1+2\sin \theta\cos \theta \\ \text{ Since }\sin ^2\theta+\cos ^2\theta=1 \end{gathered}`

So,

`((sin\theta+cos\theta)^2)/(1+2sin\theta\: cos\theta)=(1+2sin\theta\: cos\theta)/(1+2sin\theta\: cos\theta)=1`

Therefore, the correct answer is:

`((sin\theta+cos\theta)^2)/(1+2sin\theta\: cos\theta)=1`