The value of the expression (cos^2 23° – sin^2 67°) is positive.

Question

Write ‘True’ or ‘False’ and justify your answer.

The value of the expression (cos²23° – sin²67°) is positive.

Answer 1

False

Justification:

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