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: 24 cos x + 7 sin x

Philoid · Accepted Answer

Let f(x) = 24 cos x + 7 sin x

Dividing and multiplying by √(24² + 7²) = √625 = 25,

Sine of expression:

where sin α = 24/25 And cos α = 7/25

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

Cosine of the expression:

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