(a) If $\tan(\alpha + i\beta) = x + iy$, then prove that (i) $x^2 + y…
Previous year question for Engineering Mathematics-I.
Question
(a) If $\tan(\alpha + i\beta) = x + iy$, then prove that
(i) $x^2 + y^2 + 2x \cot 2\alpha = 1$,
(ii) $x^2 + y^2 - 2y \operatorname{coth} 2\beta = -1$.
(b) Prove that $\log \left[ \frac{\sin(x+iy)}{\sin(x-iy)} \right] = 2i \tan^{-1}(\cot x \tanh y)$.
- Year: 2022
- Subject: Engineering Mathematics-I
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