Show by use of a trigonometric identity that 
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Definitions:
Detection Threshold
The minimum level of intensity at which a stimulus is perceived or detected by the sensory system.
Just Noticeable Threshold
The minimum difference in stimulation that a person can detect 50% of the time; also known as the difference threshold.
Signal-detection Threshold
The sensory level at which a stimulus is detected 50% of the time, highlighting the ability to identify under conditions of uncertainty.
Psychophysics
The scientific study of the relationship between stimuli and the sensations and perceptions they produce.
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