Question

If $sin2x=\frac{2024}{2025}$, where $\frac{5\pi }{4}<x<\frac{9\pi }{4}$ , the value of the sin x - cos x is equal to

• A. $-\frac{1}{45}$
• B. $\frac{1}{45}$
• C. $\pm \frac{1}{\sqrt{2025}}$
• D. none of these

Answer 1

The correct option is C $\pm \frac{1}{\sqrt{2025}}$

Given,

$\sin 2x=\frac{2024}{2025}$

Let us consider the equation,

$(\sin x-\cos x{)}^2={\sin }^{2}x+{\cos }^{2}x-2\sin x\cos x$

$=1-\sin 2x$

$=1-\frac{2024}{2025}=\frac{1}{2025}$

$\Rightarrow \sin x-\cos x=\sqrt{\frac{1}{2025}}$

$\therefore \sin x-\cos x=\pm \frac{1}{45}$