If 5 tanθ – 4 =0, then the value of 5 sin θ – 4 cos θ/5 sinθ + 4 cos θ is

We are given the equation:
5 tanθ – 4 = 0.

Step 1: Solve for tanθ
Rearrange the equation to solve for tanθ:
5 tanθ = 4
tanθ = 4/5.

Step 2: Express sinθ and cosθ in terms of tanθ
Using the identity tanθ = sinθ / cosθ, we can write:
sinθ = 4k and cosθ = 5k,
where k is a positive constant such that sin²θ + cos²θ = 1 (Pythagorean identity).

Substitute sinθ = 4k and cosθ = 5k into the identity:
(4k)² + (5k)² = 1
16k² + 25k² = 1
41k² = 1
k² = 1/41
k = √(1/41).

Thus:
sinθ = 4k = 4/√41,
cosθ = 5k = 5/√41.

Step 3: Simplify the given expression
We are tasked with finding the value of:
(5 sinθ – 4 cosθ) / (5 sinθ + 4 cosθ).

Substitute sinθ = 4/√41 and cosθ = 5/√41 into the expression:

Numerator:
5 sinθ – 4 cosθ = 5(4/√41) – 4(5/√41)
= (20/√41) – (20/√41)
= 0.

Denominator:
5 sinθ + 4 cosθ = 5(4/√41) + 4(5/√41)
= (20/√41) + (20/√41)
= 40/√41.

Thus, the entire expression becomes:
(5 sinθ – 4 cosθ) / (5 sinθ + 4 cosθ) = 0 / (40/√41) = 0.

Step 4: Final Answer
The value of the given expression is 0.

The correct answer is:
c) zero
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.

For more please visit here:
https://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/