Write ‘True’ or ‘False’ and justify your answer.The value of t

1.	Write ‘True’ or ‘False’ and justify your answer.The value of the expression (cos223° – sin267°) is positive.
Answer» 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

Write ‘True’ or ‘False’ and justify your answer.The value of the expression (cos223° – sin267°) is positive.

Answer»

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