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Take a right angled triangle ABC with the right angle at B, so that AC is the hypotenuse.
Let AC be 1 unit long.
Using the angle CAB, the length of AC and the trigonometric ratios:
sin = opposite/hypotenuse ⇒ sin CAB = AB/AC = AB/1 = AB
cos = adjacent/hypotenuse ⇒ cos CAB = BC/AC = BC/1 = BC
Using Pythagoras:
AB2 + BC2 = AC2
⇒ (sin CAB)2 + (cos CAB)2 = 12
⇒ sin2θ + cos2θ = 1
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