Trigonometry is the branch of mathematics concerned with the functions of angles with their applications in calculations. In trigonometry, we will find six functions of an angle, namely sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), & cosecant (csc). These functions are interdependent on the kích cỡ of the triangle. These functions are used to get unknown angles và distances from the measured angles in the geometric figures.

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Trigonometry is used to compute distances và angles in different fields such as surveying, artillery, range finding, maps making, and astronomy. Problems that consist of distances and angles in a plane are covered in plane trigonometry. The problems involving distances and angles in more than one plane of three-dimensional space are covered in spherical trigonometry. In this topic, we will study the derivations và formulas of tan3A.

### What is the Formula of Tan3A?

As said earlier, trigonometry has 6 functions of an angle: sin, cos, tan, sec, cot, và csc, expressed in terms of sides of a right-angled triangle for a particular angle θ.

sinθ =

cotθ =

tanθ =

cosec θ =

secθ =

cotθ =

### Reciprocal Identities

The Reciprocal Identities are given as:

cosec θ =

sec θ =

cot θ =

sin θ =

cos θ =

tan θ =

Let us see how to lớn express multiple angles of tan3A concerning rã A or A.

The trigonometric function of tan3A concerning chảy A is called a double angle formula.

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If A is an angle, then the formula of 3A =

Now latest prove the above formula step by step:

Tan 3A =

=

=

=

=

Therefore, tan3A =

In the above formula, the angle on the right-hand side of the formula is about one-third of the left-hand side’s angle. So

tan30<^circ> =

### Conclusion

In this topic, we got khổng lồ know the detailed derivation & what is the formula of tan3A. Understand the different terms of these formulas lớn determine how lớn use them for solving trigonometric problems.