If 8 tan x = 15, then sin x – cos x is equal to
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We are given:
8 tan x = 15.
Step 1: Solve for tan x
Rearrange the equation to solve for tan x:
tan x = 15/8.
Step 2: 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 = 15k and cos x = 8k,
where k is a positive constant such that sin²x + cos²x = 1 (Pythagorean identity).
Substitute sin x = 15k and cos x = 8k into the identity:
(15k)² + (8k)² = 1
225k² + 64k² = 1
289k² = 1
k² = 1/289
k = √(1/289)
k = 1/17.
Thus:
sin x = 15k = 15/17,
cos x = 8k = 8/17.
Step 3: Find sin x – cos x
Now, calculate sin x – cos x:
sin x – cos x = (15/17) – (8/17)
= (15 – 8)/17
= 7/17.
Step 4: Final Answer
The value of sin x – cos x is 7/17.
The correct answer is:
d) 7/17
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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https://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/