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.
You might be interested in
Answer: option C
Step-by-step explanation:
The diagram of the triangle is shown in the attached photo. The triangle is a right angle triangle ABC
Assuming the given angle is #,
Recalling the trigonometric ratio,
tan # = opposite / adjacent
If tan # = 4, it means
opposite / adjacent = 4/1
Therefore, opposite = 4 and adjacent = 1
Applying Pythagoras theorem,
Hypotenuse^2 = opposite ^2 + adjacent ^2
Hypotenuse = AC
Opposite = 4
Adjacent = 1
AC^2 = 4^2 + 1^2 = 17
AC = ± √17
To determine cos #, we would apply another trigonometric ratio,
Cos# = adjacent /hypotenuse
Cos# = 1/±√17
Cos # =-1 /√17 or 1/√17
