Cosec Cot Formula

Trigonometry is a branch of mathematics concerned with the relationship between right triangle angles, heights, and lengths. This time, we'll talk about Cosec Cot Formula. Trigonometric ratios are the ratios of the sides of a right triangle. The six main ratios in trigonometry are sin, cos, tan, cot, sec, and cosec. The formulas for each of these ratios are different. It makes advantage of a right-angled triangle's three sides and angles.

What Is Cosec Cot?

For an acute angle x in a right triangle,Cosec x is given by
Cosec x = Hypotenuse / Opposite side
Cot x is given as,
Cot x = Adjacent Side/ Opposite Side
The Cosec Cot Formula as follows:
1+cot²θ=cosec²θ

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

Sol:

LHS = (cosec θ – cot θ)²
= (1/sinθ−cosθ/sinθ)²
= ((1−cosθ)/sinθ)²
RHS = (1 – cos θ)/(1 + cos θ)
By rationalising the denominator,
= (1−cosθ)/(1+cosθ)×(1−cosθ)(1−cosθ)
= (1−cosθ)²/(1−cos²θ)
= (1−cosθ)²/sin²θ
= ((1−cosθ)/sinθ)²
Therefore, LHS = RHS

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

Sol:

Using Cotangent formula we know that,
Cot P = 1 / Tan P
= 1 / (4/ 3)
= 3/4
Thus, Cot P = 3/4

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Cosec Cot Formula