What is the minimum value of p?

Calculation:

Given,

We are given the expression:

\( p = | \sin \alpha - \sin(\alpha - 90^\circ) | \)

Using the identity for sine of a difference:

\( \sin(\alpha - 90^\circ) = \cos \alpha \)

Substituting this identity into the expression for p :

\( p = | \sin \alpha - \cos \alpha | \)

The minimum value of \( | \sin \alpha - \cos \alpha | \) occurs when \(\sin \alpha = \cos \alpha \), which happens when\(\alpha = 45^\circ \). At this point:

\( \sin 45^\circ = \cos 45^\circ = \frac{1}{\sqrt{2}} \)

Therefore, at \(\alpha = 45^\circ \), the difference between \(\sin \alpha \) and \(\cos \alpha \) is 0, so:

\( p = 0 \)

∴ The minimum value of p  is 0.

Hence, the correct answer is option (a) 0.