Answer :
√3/2
Explanation:
sin A and cos A using the given information. Since tan A = opposite/adjacent = 1/√3, in a right triangle ABC, if angle A is opposite side and adjacent side is 1, the hypotenuse is √(1^2 + (1/√3)^2) = √(1 + 1/3) = √(4/3) = √4 / √3 = 2/√3.
So, sin A = opposite/hypotenuse = 1/(2/√3) = √3/2, and cos A = adjacent/hypotenuse = 1/(2/√3) = 1/(2/√3) * √3/√3 = √3/2.
Now, since angle C is the right angle, cos C = 0 and sin C = 1.
Substituting these values into the expression, we get:
sin A cos C + cos A sin C = (√3/2)(0) + (√3/2)(1) = 0 + √3/2 = √3/2.
So, sin A cos C + cos A sin C = √3/2.