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)
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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)
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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
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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
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