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Question:
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Consider the following statements:
1. The value of $\cos 46^{\circ}-\sin 46^{\circ}$ is positive.
2. The value of $\cos 44^{\circ}-\sin 44^{\circ}$ is negative.
Which of the above statement is/are correct?
Options:
1. The value of $\cos 46^{\circ}-\sin 46^{\circ}$ is positive.
2. The value of $\cos 44^{\circ}-\sin 44^{\circ}$ is negative.
Which of the above statement is/are correct?
Solution:
2607 Upvotes
Verified Answer
The correct answer is:
Neither 1 nor 2
Since $\cos \theta>\sin \theta$, in $\left[0, \frac{\pi}{4}\right]$
and $\cos \theta < \sin \theta$, in $\left[\frac{\pi}{4}, \frac{\pi}{2}\right]$
$\therefore \quad \cos 46^{\circ}-\sin 46^{\circ}=-\mathrm{ve}$
and $\cos 44^{\circ}-\sin 44^{\circ}=+\mathrm{ve}$
So, both the above statements are incorrect.
and $\cos \theta < \sin \theta$, in $\left[\frac{\pi}{4}, \frac{\pi}{2}\right]$
$\therefore \quad \cos 46^{\circ}-\sin 46^{\circ}=-\mathrm{ve}$
and $\cos 44^{\circ}-\sin 44^{\circ}=+\mathrm{ve}$
So, both the above statements are incorrect.
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