Can someone explain 9 and 10 My teacher did one problem like

4, cos 8. tan (105°) Given information about the angles, use sum or difference identities to find the trigonometric function value of the combination of the angles IL. 9. IfsinAs--where A is in quadrant IV, and cos B=-where B is in quadrant 1, find the exact value of sin(A + B). 10. If cos A where A is in quadrant I, and cos B where B is in quadrant II, 11. If sin A =-1 where A is in quadrant III, and sin B = 3 where B is in quadrant II, 12. If tan A =-12 where A is in quadrant ll, and tan B-where B is in quadrant l. find the exact value of sin(A -B). find the exact value of cos(A + B). find the exact value of tan(A +B). 13. If secAs v 50 where A is in quadrant I, and csc B =--where B is in quadrant V17 III, find the exact value of tan(A - B). 14. If sin A-13 where A is in quadrant IV, and cos B = s where Bis in quadrant 1, sin A=-- find the exact value of sin(A - B), cos (A -B), and the quadrant of angle (A - B).

Solution

9) sinA = -5/6 where A is in QIV and cosB = 4/5 where B is in QI

cosA = sqrt( 1 - sin^2A) = sqrt( 1 - 25/36) = sqrt(11)/6      (cos is +ve in QIV)

sinB = sqrt( 1 - cos^2B) = sqrt( 1 - 16/25) = 3/5         (sin is +ve in Q I)

sin(A +B) = sinAcosB + cosAsinB

plug all the values

= (-5/6)(4/5) + (sqrt(11)/6)(3/5)

= [3sqrt11 - 20]/30

10)   cosA =2/3 where A is in QI ; cosB = -1/4 where B is in QIII

sinA = sqrt( 1 - cos^2A) = sqrt( 1 -4/9) = sqrt(5)/3 ; ( sin is +ve in QI)

cosB = -1/4 ; sinB = sqrt( 1 - cos^B) = - sqrt(1 - 1/16) = - sqrt(15)/4    (sin is -ve in QIII)

sin(A - B) = sinAcosB + cosAsinB

= ( sqrt(5)/3)(-1/4) + (2/3)(-sqrt(15)/4)

= [ -sqrt(5) -2sqrt(15) ]/12