Question

If tanA=2/3 and sinB =5/√41 and angles A and B are in Quadrant I, find the value of tan (A+B) showing all steps

Answer 1

From sinB = 5/sqrt41 use trig identity sin^2+cos^2 =1 cosB = sqrt(1 - sinB^2) cosB = 4/sqrt41 tanB = sinB/cosB = 5/4 tanA = 2/3 substitute these values into above formula tan(A+B) = 23/2

Answer 2

Sin B = 5/√41
cos² B = 1 - (5/√41)²
cos ² B = 1 - 25/41
cos B = √(16/41)
cos B = 4/√41
tan B = (5/√41) : (4/√41) = 5/4
$tan ( A +B ) = \frac{tan A + tan B }{1-tanA*tanB} = \\ = \frac{2/3+5/4}{1-2/3*5/4}= \\ \frac{23/12}{1/6}= \frac{23}{2}$