Given that sin A=(sqrt22)/(5) and sin B=(sqrt7)/(3), and that angles A and B are both in Quadrant I, find the exact value of cos(A-B), in simplest radical form. Answer:

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Given that  sin A=(sqrt22)/(5) and  sin B=(sqrt7)/(3), and that angles  A and  B are both in Quadrant I, find the exact value of  cos(A-B), in simplest radical form. Answer:

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Apply cosine difference identity: Use the cosine difference identity: cos(A-B) = cos(A)cos(B) + sin(A)sin(B).Find cos(A) and cos(B): Find cos(A) and cos(B) using the Pythagorean identity: cos^2(A) = 1 - sin^2(A) and cos^2(B) = 1 - sin^2(B).Calculate cos^2(A): Calculate cos^2(A): cos^2(A) = 1 - sin^2(A) = 1 - (sqrt(22)/5)^2 = 1 - (22/25) = (25/25) - (22/25) = 3/25.Calculate cos(A): Calculate cos(A): Since A is in Quadrant I, cos(A) is positive. Therefore, cos(A) = sqrt(3/25) = sqrt(3)/5.Calculate cos^2(B): Calculate cos^2(B): cos^2(B) = 1 - sin^2(B) = 1 - (sqrt(7)/3)^2 = 1 - (7/9) = (9/9) - (7/9) = 2/9.Calculate cos(B): Calculate cos(B): Since B is in Quadrant I, cos(B) is positive. Therefore, cos(B) = sqrt(2/9) = sqrt(2)/3.Substitute values into identity: Substitute the values of cos(A), cos(B), sin(A), and sin(B) into the cosine difference identity: cos(A-B) = (sqrt(3)/5)(sqrt(2)/3) + (sqrt(22)/5)(sqrt(7)/3).Simplify the expression: Simplify the expression: cos(A-B) = (sqrt(6)/15) + (sqrt(154)/15).Combine the terms: Combine the terms: cos(A-B) = (sqrt(6) + sqrt(154))/15.

Given that $\sin A=\frac{\sqrt{22}}{5}$ and $\sin B=\frac{\sqrt{7}}{3}$ , and that angles $A$ and $B$ are both in Quadrant I, find the exact value of $\cos (A-B)$ , in simplest radical form. $\newline$ Answer:

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Given that $\sin A=\frac{\sqrt{22}}{5}$ and $\sin B=\frac{\sqrt{7}}{3}$ , and that angles $A$ and $B$ are both in Quadrant I, find the exact value of $\cos (A-B)$ , in simplest radical form. $\newline$ Answer: