The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)
How to find an expression not equivalent to a trigonometric equation
In this question we have a trigonometric equation and we are supposed to find an expression not equivalent to the former. Herein we have that the cosine of a double angle is equivalent to the following expressions:
cos 2θ = cos² θ - sin² θ (1)
cos 2θ = 2 · cos² θ - 1 (2)
cos 2θ = 1 - 2 · sin² θ (3)
The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)
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