## Cosec Cot Formula

Trigonometric ratios are the relationships between the measurements of an angle and the length. In a right-angled triangle, we have hypotenuse, base, and perpendicular. We can get the values of all six functions using these three sides.

Trigonometry is the branch of mathematics concerned with the connection between right triangle angles, heights, and lengths. This time, we’ll talk about cosec cot Formula. The ratios of the sides of a right triangle are known as trigonometric ratios. Sin, cos, tan, cot, sec and cosec are the six main trigonometric ratios. The formulae for each of these ratios are different. It takes advantage of a right-angled triangle’s three sides and angles. Let’s take a closer look at cosec cot Formulas.

## What is the cosec cot formula?

The formula for cosec x for an acute angle x in a right triangle is given by:

**cosec x = Hypotenuse / Opposite side**

cot x is given by,

**cot x = Adjacent Side / Opposite Side**

The formula for cosec cot Formula will be as given below:

1 + cot^{2}θ = cosec^{2}θ

## cosec cot formula examples

**Example 1: Prove that (cosec θ – cot θ) ^{2} = (1 – cos θ)/(1 + cos θ)**

**Solution:**

LHS = (cosec θ – cot θ)^{2}

= (1/sin θ−cosθ/sin θ)^{2}

= ((1−cos θ)/sin θ)^{2}

RHS = (1 – cos θ)/(1 + cos θ)

We now need to rationalise the denominator

= (1−cos θ)/(1+cos θ)×(1−cos θ)(1−cos θ)

= (1−cos θ)^{2}/(1−cos^{2}θ)

= (1−cos θ)^{2}/sin^{2}θ

= ((1−cos θ)/sin θ)^{2}

Therefore, LHS = RHS

**Example 2: Given that Tan P = 4 / 3, find Cot P.**

**Solution: **

According to cotangent formula:

Cot P = 1 / Tan P

= 1 / (4 / 3)

= 3/4

Thus, Cot P = 3/4