Question

The value of the expression (cos² 23° – sin² 67°) is positive.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Since, (a² – b²) = (a + b)(a – b)

cos² 23° – sin² 67° = (cos 23° + sin 67°)(cos 23° – sin 67°)

= [cos 23° + sin(90° – 23°)] [cos 23° – sin(90° – 23°)]

= (cos 23° + cos 23°)(cos 23° – cos 23°)  ...(∵ sin(90° – θ) = cos θ)

= (cos 23° + cos 23°).0

= 0, which is neither positive nor negative