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

Help me simplify I don’t understand homework and I have to show work .-example-1
User Uncle Dan
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1 Answer

1 vote

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

User Chriskilding
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