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प्रश्न
The value of the expression (cos2 23° – sin2 67°) is positive.
विकल्प
True
False
उत्तर
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
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