Cot Tan Formula

Cot Tan formula

Trigonometry, one of the most important branches of Mathematics, has many uses. Trigonometry is a branch of Mathematics that primarily focuses on the relationship between the sides and angles of right-angle triangles. The missing or unknown angles or sides of a right triangle can therefore be found by using trigonometric formulas, functions, or identities. Trigonometry allows for the expression of angles as either degrees or radians. The trigonometric angles that are used in calculations the most commonly are 0°, 30°, 45°, 60°, and 90°.

There are two other sub-branch classifications for Trigonometry. The two varieties of trigonometry are as follows:

  • Plane Trigonometry
  • Spherical Trigonometry

The Trigonometric formulas or Identities are the equations that are true in the case of Right-Angled Triangles. Some of the special trigonometric identities are given below –

Pythagorean Identities

  • sin²θ + cos²θ = 1
  • Tan2 θ + 1 = sec2θ
  • Cot2 θ + 1 = cosec2θ
  • Sin2 θ = 2 sin θ cos θ
  • Cos2 θ = cos²θ – sin²θ
  • Tan2 θ = 2 tan θ / (1 – tan²θ)
  • Cot2 θ = (cot²θ – 1) / 2 cot θ

The trigonometric angles 0°, 30°, 45°, 60°, and 90° are frequently employed in trigonometry issues. These angles’ trigonometric ratios, such as sine, cosine, and tangent, are simple to remember. Students will also display the table that lists all of the ratios and the values of each angle. Students must draw a right-angled triangle, in which one of the acute angles corresponds to the trigonometry angle, in order to obtain these angles. These angles will be described in relation to the corresponding ratio. The Cot Tan Formula has been explained below. 

In a right-angled triangle, for instance, 

Sin θ = Perpendicular/Hypotenuse

or θ = sin-1 (P/H)

Similarly,

θ = cos-1 (Base/Hypotenuse)

θ = tan-1 (Perpendicular/Base)

The sides of a right-angled triangle are divided into six trigonometric ratios. Tan is the right triangle’s base-to-altitude, and Cot Tan Formula is the right triangle’s base-to-altitude. According to the Cot Tan Formula, Cotθ and Tanθ have an inverse relationship.

The two trigonometric ratios of Cotangent and Tangent are inversely connected in this Cot Tan Formula. Tanθ is the right triangle’s base-to-altitude ratio, and Cotθ is the right triangle’s base-to-altitude altitude ratio. The Cot Tan Formula is useful for students who are solving trigonometry questions.

Cotθ = 1/Tanθ

What is the relationship between Cotθ and Tanθ?

The ratio of the Cot Tan Formula of the angle to the cos of the angle in the tangent formula is known as the law of cot or tangent, also known as the Cot Tan Formula or cot-tangent rule.

Tan Theta = Opposite Side / Adjacent Side

Cot Theta = Adjacent Side/ Opposite Side

Cot – Tan x formula

The triangle’s trigonometric ratios are also referred to as trigonometric functions. The abbreviations sin, cos, and tan stand for three essential trigonometric functions: sine, cosine, and tangent. Students would examine how these ratios or functions are evaluated in the presence of a right-angled triangle. For students who desire to answer questions correctly, the Cot Tan Formula and reference materials related to it which have been made available on the Extramarks website would prove to be helpful.

Take a look at a right-angled triangle. Its longest side is referred to as the hypotenuse, and its adjacent and opposite sides are its adjacent opposite sides.

The relationship between the lengths of the sides and angles of a right-angled triangle is the focus of the major mathematical field of trigonometry. The six trigonometric ratios or functions are sin, cos, tangent, cosec, sec, and cotangent. where a right-angled triangle’s side ratio is used to represent a trigonometric ratio. Cot Tan Formula is an important formula for students to use while they solve the questions. 

  • sin θ = opposite side/hypotenuse
  • cos θ = adjacent side/hypotenuse
  • tan θ = opposite side/adjacent side
  • cosec θ = 1/sin θ = hypotenuse/opposite side
  • sec θ = 1/cos θ = hypotenuse/adjacent side
  • cot θ = 1/tan θ = adjacent side/opposite side

The reciprocal function of the supplied tangent function is called the cotangent function. The ratio of the length of the side next to the provided angle to the length of the side across from the supplied angle determines the value of a cotangent angle in a right-angled triangle. The cotangent function is abbreviated as “cot.”

Solved Examples

There are a few examples that have been solved below with the help of Cot Tan Formula. Students will find it helpful when they will be appearing for an examination. 

  1. Show that (cosec A – sin A)(sec A – cos A) = 1/ (tan A + cot A)

LHS = (cosec A – sin A)(sec A – cos A)

= [(1/sin A) – sin A][(1/cos A) – cos A] [(1 – sin2A)/sin A] [(1 – cos2A)/cos A] = (cos2A/sin A) (sin2A/cos A)

= sin2A cos2A/sin A cos A

= sin A cos A

RHS = 1/(tan A + cot A)

= 1/[tan A + (1/tan A)] = tan A/ (tan2A + 1)

= tan A/sec2A

= tan A cos2A

= (sin A/cos A) cos2A

= sin A cos A

Therefore, LHS = RHS

(cosec A – sin A)(sec A – cos A) = 1/ (tan A + cot A)

There are a few questions that are mentioned for students to make them understand the concept of Trigonometry. Hence, they must solve the questions consistently so that they will perform better in their examination. 

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FAQs (Frequently Asked Questions)

1. What does Trigonometry's sin theta mean?

The triangle’s perpendicular to hypotenuse ratio is known as sin theta. The following contains the Sin formula.

Sinθ = Opposite side/Hypotenuse

2. Below is the Cot Tan Formula.

The Cot Tan Formula of an angle exhibit an inverse relationship with one another, as can be observed from the previous derivation.

 

As a result, CotØ × TanØ = 1.