Sum and Difference Identitiescos(a+b) =
The sum and difference identities in mathematics are trigonometric identities that relate the values of trigonometric functions for the sum or difference of two angles
The sum and difference identities in mathematics are trigonometric identities that relate the values of trigonometric functions for the sum or difference of two angles.
For the cosine function, the sum and difference identities are:
cos(a + b) = cos(a)cos(b) – sin(a)sin(b)
cos(a – b) = cos(a)cos(b) + sin(a)sin(b)
These identities can be derived using the basic definitions of trigonometric functions and the properties of right-angled triangles.
To understand these identities, let’s break down each term:
– cos(a + b): It represents the cosine of the sum of angles a and b. It is equal to the product of the cosines of the individual angles (a and b) minus the product of the sines of the individual angles. This identity is also known as the cosine of the sum.
– cos(a – b): It represents the cosine of the difference between angles a and b. It is equal to the product of the cosines of the individual angles (a and b) plus the product of the sines of the individual angles. This identity is also known as the cosine of the difference.
These identities are useful in trigonometric calculations and solving trigonometric equations. They allow us to express the cosine of a sum or difference of angles in terms of the cosine and sine of the individual angles.
Note that these identities are complementary to the sum and difference identities of the sine function, where sin(a + b) and sin(a – b) are expressed in terms of sine and cosine functions.
It’s important to practice using these identities to become comfortable with them. They are fundamental in trigonometry and can be applied in various mathematical and scientific fields.
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