The value of the expression

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.

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