Cosec Cot Formula

Trigonometry is the field of study which deals with the relationship between angles, heights, and lengths of right triangles. And this time we will be covering Cosec Cot Formula. The ratios of the sides of a right triangle are known as trigonometric ratios. Trigonometry has six main ratios namely sin, cos, tan, cot, sec, and cosec. All these ratios have different formulas. It uses the three sides and angles of a right-angled triangle. Let's look into Cosec Cot Formulas in detail.

What Is Cosec Cot Formula?

Let's look into the Cosec Cot Formula

For an acute angle x in a right triangle, Cosec x is given by

Cosec x = Hypotenuse / Opposite side

Cot x is given by,

Cot x = Adjacent Side / Opposite Side

The Cosec Cot Formula is given as follows:

\(1+\cot ^{2} \theta=\operatorname{cosec}^{2} \theta\)

Examples using Cosec Cot Formula

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)

By rationalising the denominator,

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

= (1−cos θ)²/(1−cos²θ)

= (1−cos θ)²/sin²θ

= ((1−cos θ)/sin θ)²

Therefore, LHS = RHS

Example 2: Find Cot P if Tan P = 4 / 3

Solution: 

Using Cotangent formula we know that,

Cot P = 1 / Tan P

= 1 / (4 / 3)

= 3/4

Thus, Cot P = 3/4