If 90o<A<180o and sinA=4/5, then tanA/2 is equal to
To find the value of tan(A/2), we can use the half-angle formula for tangent:
tan(A/2) = (1 - cos(A))/sin(A)
Since we know that sin(A) = 4/5, we can find cos(A) using the Pythagorean identity:
sin^2(A) + cos^2(A) = 1
(4/5)^2 + cos^2(A) = 1
16/25 + cos^2(A) = 1
cos^2(A) = 1 - 16/25
cos^2(A) = 9/25
cos(A) = ±√(9/25)
cos(A) = ±3/5
Since A is in the second quadrant (90° < A < 180°), cos(A) is negative.
Therefore, cos(A) = -3/5.
Now, we can substitute these values back into the formula for tan(A/2):
tan(A/2) = (1 - cos(A))/sin(A)
= (1 - (-3/5))/(4/5)
= (5/5 + 3/5)/(4/5)
= 8/4
= 2
Therefore, tan(A/2) = 2.