(a) If $a + ib = c \tan(x + iy)$ then prove that $\tan 2x = \frac{2ac…

Previous year question for Engineering Mathematics-I.

Question

(a) If $a + ib = c \tan(x + iy)$ then prove that $\tan 2x = \frac{2ac}{c^2 - a^2 - b^2}$.

(b) Sum the following series:

$$1 + \frac{\cos \alpha}{\cos \alpha} + \frac{\cos 2\alpha}{2! \cos^2 \alpha} + \frac{\cos 3\alpha}{3! \cos^3 \alpha} + \dots$$

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