If 16 cot x = 12, then sin x – cos x/ sin x + cos x equals

We are given:
16 cot x = 12.

Step 1: Solve for cot x
Rearrange the equation to solve for cot x:
cot x = 12/16 = 3/4.

Step 2: Express tan x in terms of cot x
Using the identity cot x = 1/tan x, we can write:
tan x = 1/cot x = 1/(3/4) = 4/3.

Step 3: Express sin x and cos x in terms of tan x
Using the identity tan x = sin x / cos x, we can write:
sin x = 4k and cos x = 3k,
where k is a positive constant such that sin²x + cos²x = 1 (Pythagorean identity).

Substitute sin x = 4k and cos x = 3k into the identity:
(4k)² + (3k)² = 1
16k² + 9k² = 1
25k² = 1
k² = 1/25
k = √(1/25)
k = 1/5.

Thus:
sin x = 4k = 4/5,
cos x = 3k = 3/5.

Step 4: Simplify the given expression
We are tasked with finding the value of:
(sin x – cos x) / (sin x + cos x).

Substitute sin x = 4/5 and cos x = 3/5 into the expression:

Numerator:
sin x – cos x = (4/5) – (3/5)
= (4 – 3)/5
= 1/5.

Denominator:
sin x + cos x = (4/5) + (3/5)
= (4 + 3)/5
= 7/5.

Thus, the entire expression becomes:
(sin x – cos x) / (sin x + cos x) = (1/5) / (7/5).

Simplify:
(1/5) / (7/5) = 1/7.

Step 5: Final Answer
The value of (sin x – cos x) / (sin x + cos x) is 1/7.

The correct answer is:
a) 1/7
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.

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