Find the exact value using double angle or reduction formula

Question

Sin A = 0.6 and A is obtuse Sin B = 0.8 and B is acute What is the exact value of cos(A+B)?

Answer 1

A would be sin^-1(.6)=about 37.86 degrees if acute, as obtuse it's about 180-37.86 = 142.14

B = sin^-1(.8)= about 90-37.86 = 53.13

C(142.14+53.13)=Cos195.27=-Cos15.27= about -0.9647

but exactly -0.96

sinA=0.6 =3/5, cosA=-4/5

sinB=0.8=4/5, cosB=3/5

Cos(A+B) = cosAcosB - sinAsinB

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

= -24/25

=-0.96

Answer 2

sin A = 0.6 and is obtuse therefore A is in QII. What is cos A?

Now use cosine of sum formula.