Question
Write 'True' or 'False' and justify your answer in the following:
The value of the expression $\sin80^\circ-\cos80^\circ$ is negative.
The value of the expression $\sin80^\circ-\cos80^\circ$ is negative.
✓
Answer
False.
$\sin80^\circ-\cos80^\circ$
$=\sin80^\circ-\sin(90^\circ-80^\circ)$
$=\sin80^\circ-\sin10^\circ\text{is }+\text{ve} $
$\because\ \sin\theta$ increase as $\theta$ increase.
$\sin80^\circ-\cos80^\circ$
$=\sin80^\circ-\sin(90^\circ-80^\circ)$
$=\sin80^\circ-\sin10^\circ\text{is }+\text{ve} $
$\because\ \sin\theta$ increase as $\theta$ increase.
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