First slide

Trigonometric Identities

Question

The value of the function $sgn (\cos x - \sin x) in x \in (\frac{π}{4}, \frac{π}{2}) =$
( sgn is Signum function)

Easy

A

0
B

1
C

2
D

-1

Solution

$\begin{array}{l} In (\frac{π}{4}, \frac{π}{2}), \cos x < \sin x \\ \Rightarrow \cos x - \sin x < 0 \\ ∴ sgn (\cos x - \sin x) = - 1 \end{array}$

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