SOLUTION: Given: cos A = 3/5, tan B = 12/5, A is in Quadrant 1 and is in Quadrant 3 Find 1.Sin (A + B) 2.Sin (A - B) 3.Cos (A + B) 4.Cos (A - B) 5.Tan (A

SOLUTION: Given: cos A = 3/5, tan B = 12/5, A is in Quadrant 1 and is in Quadrant 3 Find 1.Sin (A + B) 2.Sin (A - B) 3.Cos (A + B) 4.Cos (A - B) 5.Tan (A - B) 6.Tan ( A+ B)

Question 1181125: Given: cos A = 3/5, tan B = 12/5, A is in Quadrant 1 and is in Quadrant 3
Find
1.Sin (A + B)
2.Sin (A - B)
3.Cos (A + B)
4.Cos (A - B)
5.Tan (A - B)
6.Tan ( A+ B)
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
cos A = 3/5, A is in Quadrant 1
sin A =4/5 , cos A = 3/5 , tan A =4/3

tan B = 12/5, quadrant IV
tan B = -12/5, sin B = -12/13 , cos B = 5/13
Sin (A + B) = sin(a)cos(b) + cos(a)sin(b)
= (4/5)(5/13) +(3/5)(-12/13)
= 20/65 - 36/65
-16/65

sin(A − B) = sin A cos B − cos A sin B
=(4/5)(5/13) -(3/5)(-12/13)
56/65
cos(A + B) = cos A cos B − sin A sin B
cos(A − B) = cos A cos B + sin A sin B
sin(A + B) = sin A cos B + cos A sin B
Plug values and continue

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

            The numbers and calculations in the post by @mananth are INCORRECT.

            Therefore, for your safety, IGNORE his (or her) post.

            I came to bring a correct solution.

cos A = , A is in Quadrant 1 sin A = = = = = , cos A = , tan A = tan B = , quadrant III ( ! not quadrant IV, as @mananth mistakenly wrote ! ) tan B = , sin B = , cos B = sin (A + B) = sin(A)cos(B) + cos(A)sin(B) = + = - = . sin(A − B) = sin(A)*cos(B) − cos(A)*sin(B) = - = + = . cos(A + B) = cos A cos B − sin A sin B cos(A − B) = cos A cos B + sin A sin B sin(A + B) = sin A cos B + cos A sin B Plug values and continue

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    - Evaluating trigonometric expressions
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