How to Prove the Trigonometric Identities for Sin and Cos of A+B?

In summary, trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Its main purpose is to help solve problems involving triangles, such as finding missing sides or angles. The three basic trigonometric ratios are sine, cosine, and tangent, which represent the relationship between the sides of a right triangle and its angles. Trigonometry has various real-world applications, including engineering, navigation, architecture, and physics. It is also used in fields like astronomy, surveying, and even music and art. The difference between radians and degrees in trigonometry is that degrees are based on a circle divided into 360 equal parts, while radians are based on the radius of a circle. To solve a
  • #1
basty
95
0
Why

##\sin (A+B) = \sin A \cos B + \cos A \sin B##

and

##\cos (A+B) = \cos A \cos B - \sin A \sin B##

??
 
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  • #2
The proof of this should be available in any basic textbook on trigonometry or by a simple search in a search engine. I suggest starting here: http://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities
Please note that Physics Forums is not a substitute for a textbook or intended to spoon feed you basic mathematical facts.
 

FAQ: How to Prove the Trigonometric Identities for Sin and Cos of A+B?

What is the purpose of trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Its main purpose is to help solve problems involving triangles, such as finding missing sides or angles.

What are the three basic trigonometric ratios?

The three basic trigonometric ratios are sine, cosine, and tangent. These ratios represent the relationship between the sides of a right triangle and its angles.

How is trigonometry used in real life?

Trigonometry has numerous real-world applications, such as in engineering, navigation, architecture, and physics. It is also used in fields like astronomy, surveying, and even music and art.

What is the difference between radians and degrees in trigonometry?

Radians and degrees are two units of measurement used in trigonometry to measure angles. Degrees are based on a circle divided into 360 equal parts, while radians are based on the radius of a circle. One radian is equal to approximately 57.3 degrees.

How can I solve a trigonometry question?

To solve a trigonometry question, you can use the trigonometric ratios and the Pythagorean theorem. First, identify the given information and the unknown value. Then, choose the appropriate trigonometric ratio and set up an equation to solve for the unknown value. Finally, use algebra to solve for the unknown value.

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