Reduce each of the following expressions to the Sine And Cosine ofA single expression:

Question

Reduce each of the following expressions to the Sine And Cosine ofA single expression: cos x – sin x

Philoid · Accepted Answer

Let f(x) = cos x – sin x

Dividing and multiplying by √(1 + 1) = √2,

Sine of expression:

We know that sinA cosB – cosA sinB = sin(A –B)

Cosine of the expression:

We know that cosA cosB – sinA sinB = cos(A +B)