a. $\cos{z} = \cos2$
b. $\cosh z = \cosh2$
c. $\cos z = \cosh2$
d.$\sin z = \sinh2$
e. $\cosh z = \sin2$
f. $cos z = -1$
g. $cos z = 2$
h. $\cosh z = 2i$
i. $\sinh z = 4i$
j. $\cos z + \sin z = i$
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Use http://math.stackexchange.com/questions/3510/how-to-prove-eulers-formula-eit-cos-t-i-sin-t – lab bhattacharjee Mar 25 '17 at 02:13
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Welcome to Math.SE. Please take the tour (http://math.stackexchange.com/tour) to get acquainted with this site. In particular, please include your efforts on the problem. – martin.koeberl Mar 25 '17 at 02:23
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2Welcome to Math SE! It is recommended that you provide the work you have done so that people can help you better. As suggested by others, please invest a minute of your time to take the tour of the site and look at how to format mathematics on Math SE. Furthermore, I suggest that you bookmark this very useful MathJax link for quick reference. Cheers! – Mar 25 '17 at 02:26
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Hint: You can use Euler's formula $$e^{i\theta}=\cos\theta+i\sin\theta$$ and other identities \begin{eqnarray} \sin\theta&=&\dfrac{e^{i\theta}-e^{-i\theta}}{2i}\\ \cos\theta&=&\dfrac{e^{i\theta}+e^{-i\theta}}{2}\\ \sinh\theta&=&\dfrac{e^{\theta}-e^{-\theta}}{2}\\ \cosh\theta&=&\dfrac{e^{\theta}+e^{-\theta}}{2} \end{eqnarray} $$\cosh \theta=\cos i\theta~~~;~~~i\sinh\theta=\sin i\theta$$ here you find some properties of trigonometric and hyperbolic functions. Also here helps you more. There are many solved examples in this site like this, this and this. After your works we wait for your attempts on these problems and you are welcome.
