The value of the expression \(\cos^2 23^\circ-\sin^2 67^\circ\) is positive.
False.
Step 1: Recall the trigonometric identity: \(\sin(90^\circ - \theta) = \cos \theta\).
Step 2: Here, we have \(\sin 67^\circ\). Notice that \(67^\circ = 90^\circ - 23^\circ\).
Step 3: So, \(\sin 67^\circ = \sin(90^\circ - 23^\circ) = \cos 23^\circ\).
Step 4: Substitute this value into the expression: \(\cos^2 23^\circ - \sin^2 67^\circ = \cos^2 23^\circ - (\cos 23^\circ)^2\).
Step 5: Simplify: \(\cos^2 23^\circ - \cos^2 23^\circ = 0\).
Step 6: The result is \(0\). Since 0 is neither positive nor negative, the statement “the value is positive” is False.