Question

For Positive Acute Angles A And B, It Is Known That Tan A= 60/11 And Cos B= 24/25. Find The Value Of Sin A+B In the Simplest Form. 50 Answer: X=Frac Square Square Hit Answer

Answer 1

We can use the trigonometric identity sin(A+B) = sinAcosB + cosAsinB to find sin(A+B).

First, we need to find sinA and sinB. We can use the Pythagorean identity to find sinA:
sin^2 A + cos^2 A = 1
sin^2 A + (60/11)^2 = 1
sin^2 A = 1 - (60/11)^2
sin A = sqrt(1 - (60/11)^2)

Similarly, we can use the Pythagorean identity to find sinB:
sin^2 B + cos^2 B = 1
sin^2 B + (24/25)^2 = 1
sin^2 B = 1 - (24/25)^2
sin B = sqrt(1 - (24/25)^2)

Now we can use the identity sin(A+B) = sinAcosB + cosAsinB:
sin(A+B) = sinAcosB + cosAsinB
sin(A+B) = sqrt(1 - (60/11)^2) * (24/25) + (60/11) * sqrt(1 - (24/25)^2)

We can simplify this expression by using the fact that 60/11 = (120/22) = (240/44) and 24/25 = (48/50) = (96/100):
sin(A+B) = sqrt(1 - (240/121)^2) * (96/100) + (240/121) * sqrt(1 - (96/100)^2)
sin(A+B) = (sqrt(14561) / 121) * (24/25) + (240/121) * (7/25)
sin(A+B) = (576 * sqrt(14561) + 1680) / 3025

Therefore, sin(A+B) = (576 * sqrt(14561) + 1680) / 3025.

Hope this helps