By applying fundamental trigonometry and the values for common angles, we have that (1 - cos² 60°) · (1 + cos² 300°) is equivalent to 2 · sin² 120° + sin⁴ 60°.
How to determine an equivalent trigonometric expression by means of formulas
In this question we have to prove the trigonometric expression by means of fundamental trigonometric relationships and known values for certain angles. We proceed to prove that one side of the expression is equivalent to the other side:
- (1 - cos² 60°) · (1 + cos² 300°) Given
- sin² 60° · (2 - sin² 300°) sin² α + cos² α = 1
- 2 · sin² 60° - sin² 60° · sin² 300° Distributive property
- 2 · sin² 120° + sin⁴ 60° Sine is an odd function/Result
By applying fundamental trigonometry and the values for common angles, we have that (1 - cos² 60°) · (1 + cos² 300°) is equivalent to 2 · sin² 120° + sin⁴ 60°.
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