# Question Video: Using Angle-Sum and -Difference Identities to Simplify Trigonometric Expressions Mathematics • 10th Grade

Simplify cos 2π cos 22π β sin 2π sin 22π.

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### Video Transcript

Simplify cos of two π times cos of 22π minus sin of two π times sin of 22π.

When we look at this expression, we see that we have the angle two π and the angle 22π. We have the cos and sin of the angle two π, and we have the cos and sin of the angle 22π, which means we have an expression in the form cos of π΄ times cos of π΅ minus sin of π΄ times sin of π΅. And we can simplify this expression using the angle sum identities. We know that the cos of π΄ times the cos of π΅ minus the sin of π΄ times the sin of π΅ is equal to the cos of π΄ plus π΅. In our case, the angle π΄ is two π and the angle π΅ is 22π, making this expression equal to cos of two π plus 22π, cos of 24π. And so the simplified form of this expression is cos of 24π.