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JAMB Mathematics 2024 Paper

Question : 32

Total: 50

Differentiate Cos25º - Sin 25º

Solution:

Concept:

Apply the standard derivatives of sine and cosine to the angle expression, then evaluate at

25^\circ

Explanation:

Treat the expression as

y = \cos \theta - \sin \theta

Differentiate term by term with respect to

\theta

The derivative of

\cos \theta

-\sin \theta

The derivative of

-\sin \theta

-\cos \theta

So,

\frac{dy}{d\theta} = -\sin \theta - \cos \theta

Factor out the negative sign:

\frac{dy}{d\theta} = -(\sin \theta + \cos \theta)

Now substitute

\theta = 25^\circ

\frac{dy}{d\theta} = -(\sin 25^\circ + \cos 25^\circ)

This corresponds to option A.

Answer:

-(\sin 25^\circ + \cos 25^\circ)

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