# Tangent sum and difference formula We can also use the tangent formula to find the angle between two lines. We will get two cases which are supplementary to each other. To find the angle in.

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Angle addition formulas express trigonometric functions of sums of angles in terms of functions of and. The fundamental formulas of angle addition in trigonometry are given by. The first four of these are known as the prosthaphaeresis formulas , or sometimes as Simpson's formulas. The sine and cosine angle addition identities can be compactly summarized by the matrix equation. These formulas can be simply derived using complex exponentials and the Euler formula as follows. Equating real and imaginary parts then gives 1 and 3 , and 2 and 4 follow immediately by substituting for.

You have seen quite a few trigonometric identities in the past few pages. It is convenient to have a summary of them for reference. The more important identities. But these you should. Defining relations for tangent, cotangent, secant, and cosecant in terms of sine and cosine. The Pythagorean formula for sines and cosines. This is probably the most important trig identity.

In the problem below, and. Since and is in quadrant I, we can say that and and therefore:. Using the tangent sum formula, we see:. Given that and , find. Which of the following expressions best represents? Write the identity for.

## Tangent Identities

First, allow us to introduce you to the sine sum and difference identities. Things are definitely moving here in trig land.

## 7.2: Sum and Difference Identities

How can the height of a mountain be measured? What about the distance from Earth to the sun? Like many seemingly impossible problems, we rely on mathematical formulas to find the answers. The trigonometric identities, commonly used in mathematical proofs, have had real-world applications for centuries, including their use in calculating long distances. The trigonometric identities we will examine in this section can be traced to a Persian astronomer who lived around AD, but the ancient Greeks discovered these same formulas much earlier and stated them in terms of chords. These are special equations or postulates, true for all values input to the equations, and with innumerable applications.

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