# Tagged Questions

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### Proving $\left(\frac{1+\sin x+i\cos x}{1+\sin x-i\cos x}\right)^n=\cos n\left(\frac{\pi }{2}-x\right)+i\sin n\left(\frac{\pi }{2-x}\right)$

How to solve the following question? If $n$ is an integer, show that \begin{eqnarray} \left(\frac{1+\sin x+i\cos x}{1+\sin x-i\cos x}\right)^n=\cos n\left(\frac{\pi }{2}-x\right)+i\sin ...
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### Can a complex number have two arguments

Now, the reason why I wrote two $\theta$s is because my answer is the answer we get from $\theta$2 and the answer in the book is given the value of $\theta$1. So, I was just wondering whether both ...
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### Trignometric problem (using De Movier's Theorem)

Ok so this question, I started out writing tan as sin and cos in the right side of the equation, simplified as much as possible and ended up with a very (sort of) fascinating equation which is ...
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### Question regarding in periodic function

I have question I know that $\cos(x+2\pi)=\cos x$ and $\sin(x+2\pi)=\sin x$ but if we have $\cos(x+\pi)=?$ and $\sin(x+\pi)=?$ with explaination thanks
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### Find all values for cos(i)

In my Differential Equations class recently we have learned about Euler's Formula and Fourier Series. I am given the problem ...
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### Lengthy Product of trigonometric ratios

What is the value of the product $\sin(10) \sin(20) \sin(30) \sin(40) \sin(50) \sin(60) \sin(70) \sin80$, where all the angles are in degrees? Solve using complex numbers. I found this in a book of ...
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### Express $\sin 3\theta$ and $\cos 3\theta$ as functions of $\sin \theta$ and $\cos \theta$ using Euler's identity
Using Euler's identity ($e^{in\theta}=\cos n\theta+i \sin n\theta$), express $\sin 3\theta$ and $\cos 3\theta$ as functions of $\sin \theta$ and $\cos \theta$. Any ideas?