Verify the identity sec(theta)sin(theta)cot(theta) = 1
1 answer:
Secant = hypotenuse / adjacent
sine = opposite / hypotenuse
cotangent = adjacent / opposite
So, if we multiply all three we have a numerator of
hypotenuse * opposite * adjacent and a denominator of
adjacent * hypotenuse * opposite
Notice that "hypotenuse", "opposite", and "adjacent" appear exactly once in the numerator AND the denominator.
When numerator = denominator, then a fraction equals ONE.
sine = opposite / hypotenuse
cotangent = adjacent / opposite
So, if we multiply all three we have a numerator of
hypotenuse * opposite * adjacent and a denominator of
adjacent * hypotenuse * opposite
Notice that "hypotenuse", "opposite", and "adjacent" appear exactly once in the numerator AND the denominator.
When numerator = denominator, then a fraction equals ONE.
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