Question

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Answer 1

Concept used

• cos(z) = $\dfrac{e^{iz}\:+\:e^{-iz}}{2}$

• sin(z) = $\dfrac{e^{iz}\:-\:e^{-iz}}{2i}$

• $e^{i\theta}\:=\: \cos(\theta)\:+\:i\sin(\theta)$

• x + iy = a + ib implies x = a and y = b.

• Compodendo-dividendo is used to make out the expression for $e^{i2\phi}$ so that we can take log and seperate out $\phi$ whose value we have to find.

• In last step, we have used trigonometric substitution so that we get the required expression for $\phi$.

• While solving questions based on this topic, it is always advisable to convert rectangular/trigonometric form into $e^{i\theta}$ form.

Answer 2

Answer hope it's help you...