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  • The value of the expression (sin 80° – cos80°) is negative.

The value of the expression (sin 80° – cos80°) is negative.

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Answer.     [False]
Solution.     (sin 80° – cos 80°)
We know that from 0 to 90° sin\theta  and cos\theta  both are positive i.e.
0< \sin \theta \leq 90^{\circ}  (always positive)
 0< \cos \theta \leq 90^{\circ} (always positive)
At 45° both the values of sin\theta  and cos\theta  are the same but after 45° to 90° value of sin is greater than the value of cos\theta Hence sin 80° > cos 80°.
If we subtract a smaller term from bigger than the result is positive.
Hence (sin 80° – cos80°) > 0
So, the given statement is false

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