Let sin A = 12/13 with 90º≤ A≤ 180º and tan B = -4/3 with 270º≤ B≤ 360º. Find tan ( A + B ).
16/63
56/33
-63/65
-65/56
A?
nope
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I did 2 like this for Bri below
have to go to library meeting now
To find the value of tan(A + B), we can use the trigonometric identity:
tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)
First, let's find the value of tan A and tan B:
Given: sin A = 12/13
To find tan A, we can use the relationship between sine and cosine:
cos A = √(1 - sin^2 A) = √(1 - (12/13)^2) = √(1 - 144/169) = √(25/169) = 5/13
tan A = sin A / cos A = (12/13) / (5/13) = 12/5
Given: tan B = -4/3
Now, we can substitute the values of tan A and tan B into the trigonometric identity:
tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)
= (12/5 + (-4/3)) / (1 - (12/5) * (-4/3))
= (36/15 - 20/15) / (1 + 16/15)
= 16/15 / (31/15)
= 16/15 * 15/31
= 16/31
Therefore, tan(A + B) = 16/31.
None of the provided options match this result, so "None of the above" would be the correct answer.