Answer to Question #162890 in Trigonometry for Aldryan venth

Question #162890

Cos(5x)cos(2x) + sin(5x)sin(2x)

Expert's answer

Use the angle subtraction formula for cosine:

"\\cos(\\alpha-\\beta)=\\cos\\alpha\\cos\\beta+\\sin\\alpha\\sin\\beta"

Let

"\\alpha=5x", "\\beta=2x".

Then

"\\cos5x\\cos2x+\\sin5x\\sin2x=\\cos(5x-2x)=\\cos3x"

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