If tan A = 3/4, then sin A cos A = 12/25.
Answer (1)
To solve the problem, we are given that tan A = 4 3 . We need to determine whether sin A cos A = 25 12 is true.
Step-by-step:
Understanding Tangent : Given that tan A = 4 3 , we know the relationship between the sides of a right triangle:
Opposite side: 3
Adjacent side: 4
Finding the Hypotenuse : We use the Pythagorean theorem to find the hypotenuse c :
c = 3 2 + 4 2 = 9 + 16 = 25 = 5
Calculating Sine and Cosine :
sin A = Hypotenuse Opposite = 5 3
cos A = Hypotenuse Adjacent = 5 4
Compute sin A cos A :
sin A cos A = ( 5 3 ) ( 5 4 ) = 25 12
Therefore, sin A cos A = 25 12 is indeed true.
