Does 1 - (tan 25 degs)(tan 110 degs) equal 1? If so, how?
of course not.
If 1-u = 1, then u=0. Unless one of those tan values is zero, the assertion is false.
The tangent of 25 degrees is in quadrant I, this means that the tangent is going to have a positive value. The tangent of 110 degrees is in quadrant II and will have a negative value. If you multiply a negative by a positive, the end product is a negative.
1- (said negative #) =
1+(the number)=
Therefore the sides are not equal.
Verdict: False; cannot be equal to 1.
To determine whether 1 - (tan 25 degrees)(tan 110 degrees) equals 1, we can first simplify the expression using trigonometric identities and then evaluate it.
We know that the tangent of the sum of two angles, A + B, can be represented as (tan A + tan B) / (1 - tan A * tan B). Applying this identity:
(tan 25 degrees + tan 110 degrees) / (1 - tan 25 degrees * tan 110 degrees)
To evaluate this expression, we can use a scientific calculator or trigonometric table to find the values of tangent for 25 and 110 degrees:
tan 25 degrees ≈ 0.4663
tan 110 degrees ≈ -1.9952
Substituting these values into the expression:
(0.4663 + (-1.9952)) / (1 - 0.4663 * (-1.9952))
Simplifying further:
-1.5289 / (1 + 0.9307)
= -1.5289 / 1.9307
≈ -0.7920
Therefore, 1 - (tan 25 degrees)(tan 110 degrees) is approximately equal to -0.7920, which is not equal to 1.