Question

If Sin A = /, Cos B = -/5, A is in the II quadrant and B is in the III quadrant , find

Sin (A+B) & Cos (A+B)​

Answer 1

Answer:

sin(A+B) =16/35

cos(A+B) =33/65

Step-by-step explanation:

Please

If Sin A = 4/5, Cos B = -5/13, A is in the II quadrant and B is in the III quadrant , find

Sin (A+B) & Cos (A+B)​

*****************************************************

A is in the II quadrant and B is in the III quadrant

Then Sin A=4/5 is +ve

and cosA,CosB and SinB are -ve

Cos A=-√(1-16/25) =-√9/25= -3/5

CosB= -5/13

sinB=-√1-25/169=-√144/169= -12/13

sin(A+B) = sinAcosB + sinBcosA

=4/5(-5/13) + (-12/13)(-3/5)

= -4/13 +36/65

=(-20+36)/65=16/35

sin(A+B) =16/35

*************

Now Cos(A+B)=cosAcosB - sinAsinB

=(-3/5)(-5/13) - (4/5)(-12/13)

=3/13+48/65

=(-15+48)/65

=33/65

cos(A+B) =33/65