Question

if cot theta = a/b then find the value of cos theta - sin theta / cos theta + sin theta.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

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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