Question 1194315
 If tan A = ¾ and cos B = 12/13, find
a. Tan (A  -  B)
b. c. tan ( B  -  A )
c. Sin ( A + B)
d. cos 2A
<pre>           {{{matrix(1,7, tan (A), "=", O/A, "=", 3/4, "=", y/x)}}}    {{{matrix(1,7, cos (B), "=", A/H, "=", 12/13, "=", x/r)}}}              
This is a 3-4-5 Pythag. Triple,    This is a 5-12-13 Pythag. Triple,
      so <font color = red><font size = 3><b>hypotenuse = H = r = 5</font></font></b>    so <font color = red><font size = 3><v>opposite = O = y = 5</font></font></b>   
Therefore, {{{matrix(2,7, cos (A), "=", A/H, "=", x/r, "=", 4/5, sin (A), "=", O/H, "=", y/r, "=", 3/5)}}}    Therefore, {{{matrix(2,7, tan (B), "=", O/A, "=", y/x, "=", 5/12, sin (B), "=", O/H, "=", y/r, "=", 5/13)}}}

<font color = red><font size = 4><b>a. {{{matrix(1,3, tan (A - B), "=", (tan (A) - tan (B))/(1 + tan (A) tan (B)))}}}</font></font></b>
    Make the necessary substitutions and you should have the answer.

<font color = red><font size = 4><b>b. {{{matrix(1,3, tan (B - A), "=", (tan (B) - tan (A))/(1 + tan (B) tan (A)))}}}</font></font></b>
    Make the necessary substitutions and you should have the answer, 
    or
    Simply NEGATE a.

<font color = red><font size = 4><b>c. sin (A + B) = sin (A) cos (B) + cos (A) sin (B)</font></font></b>
    Make the necessary substitutions and you should have the answer.

<font color = red><font size = 4><b>d. {{{system(matrix(1,3, cos (2A), "=", cos^2 (A) - sin^2 (A)), or, matrix(1,3, cos (2A), "=", 2 * cos^2 (A) - 1), or, matrix(1,3, cos (2A), "=", 1 - 2 * sin^2 (A)))}}}</font></font></b>
    Make the necessary substitutions and you should have the answer.</pre>