if cot theta = a/b then find the value of cos theta - sin theta / cos theta + sin theta.
Answers
Answer:
Step-by-step explanation:
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Concept:
Trigonometry is the relation between the angles of a triangle.
Trigonometric functions include: sine function, cosine function, tangent function, co-tangent function, secant function and co-secant function.
The Pythagoras theorem defines the relation between the sides of the right angled triangle.
Given:
We are given the function:
cot θ=a/b.
Find:
We need to find the value of the function:
(cosθ-sin)/(cosθ+sinθ)
Solution:
We know that cot θ= base / perpendicular.
So, we get the base=a and perpendicular=b.
By using Pythagoras theorem, we get that:
Hypotenuse=√a²+b²
Cosθ= base/hypotenuse =a/√a²+b²
sinθ=perpendicular/hypotenuse=b/√a²+b²
The value of (cosθ-sin)/(cosθ+sinθ) is:
=(a/√a²+b²-b/√a²+b²)/(a/√a²+b²+b/√a²+b²)
=(a-b)/(a+b)
Therefore, we get the value of (cosθ-sin)/(cosθ+sinθ) as (a-b)/(a+b) when cot θ=a/b.
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