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Find the differentiation of f(x) = cos (x - a)


1. cos x cos a + sin x sin a 
2. sin x cos a - cos x sin a
3. cos x sin a - sin x cos a
4. cos x sin a + sin x cos a

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Correct Answer - Option 3 : cos x sin a - sin x cos a

Concept:

cos (x + y) = cos x cos y - sin x sin y

cos (x - y) = cos x cos y + sin x sin y

sin (x + y) = sin x cos y + cos x sin y 

sin (x - y) = sin x cos y - cos x sin y 

Calculation:

\(\rm \frac{\mathrm{d} \cos (x - a)}{\mathrm{d} x}\)

= -sin (x - a)

= -[sin x cos a - cos x sin a]

= cos x sin a - sin x cos a

∴ The required value is cos x sin a - sin x cos a

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