Question Video: Simplifying Trigonometric Expressions Using the Sum and Difference of Angles Identities | Nagwa Question Video: Simplifying Trigonometric Expressions Using the Sum and Difference of Angles Identities | Nagwa

# Question Video: Simplifying Trigonometric Expressions Using the Sum and Difference of Angles Identities

Simplify cos (π΄ β π΅) β cos (π΄ + π΅).

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### Video Transcript

Simplify cos π΄ minus π΅ minus cos π΄ plus π΅.

In order to simplify this expression, we firstly need to recall two of our compound-angle identities. Cos π΄ minus π΅ is equal to cos π΄ cos π΅ plus sin π΄ sin π΅. Cos π΄ plus π΅, on the other hand, is equal to cos π΄ cos π΅ minus sin π΄ sin π΅. We can now substitute these identities into our expression. Our expression becomes cos π΄ cos π΅ plus sin π΄ sin π΅ minus cos π΄ cos π΅ minus sin π΄ sin π΅.

As weβre subtracting the two terms inside the parentheses, this simplifies to become negative cos π΄ cos π΅ plus sin π΄ sin π΅. Subtracting a negative term produces a positive term. At this stage, we can then collect or group like terms. Cos π΄ cos π΅ minus cos π΄ cos π΅ is equal to zero. Sin π΄ sin π΅ plus sin π΄ sin π΅ is equal to two sin π΄ sin π΅. This is the simplified version of cos π΄ minus π΅ minus cos π΄ plus π΅.

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