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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Frequently Asked Questions
In trigonometry, the cosecant (csc\csccsc) and cotangent (cot\cotcot) functions are related through the identity:
csc2θ=1+cot2θ
This formula is derived from the Pythagorean identity and is useful in solving trigonometric equations and integrals.
The identity csc2θ=1+cot2θ helps simplify expressions involving cosecant and cotangent. It is widely used in calculus, physics, and engineering problems where trigonometric transformations are required.