Question

If tan (a-b)=7/24 and tan a= 4/3 where a and b are in the first quadrant prove that a+b= pi/2

Answer 1

In order to solve this sums we need to know the formula of tan(a-b)

tan(a - b) = (tan a - tan b)/(1+(tan a x tan b)) = 7 / 24 (given)

24 tan a - 24 tan b = 7 + 7 tan a tan b

24 x 4/3 - 24 tan b = 7 + 7 4/3 tan b

32 - 24 tan b = 7 + (28 tan b / 3)

28 tan b + 72 tan b = 75

100 tan b = 75

tan b = 75/100 = 3/4

for tan A

p = perpendicular = 4

b = base = 3

h = height = 5

for tan B

p = perpendicular = 3

b = base = 4

h = height = 5

we have to prove (a + b) = 90 degree.

sin (a + b) = sin 90 degree = 1

or sin a cos b + sin b cos a = 16/25 + 9/25 = 25/25 = 1 = RHS [Proved].

Answer 2

Answer:

Step-by-step explanation: