Question:
The value of the expression (cos2 23° – sin2 67°) is positive.
Solution:
False
cos223° – sin2 67°= (cos23° – sin67°)(cos23° + sin67°) [∴(a2 – b2) = (a – b) (a + b)]
= [cos23° – sin (90° – 23°)] (cos23° + sin67°)
= (cos23° – cos23°) (cos23° + sin67°) [∴sin (90° – 0) = cos 0]
= 0.(cos23° + sin67°) = 0
which may be either positive or negative.