Question

find cos(alpha-beta) if sin alpha=2/3 and cos beta=3/4 and alpha lies in 2nd quadrant and beta lies in 4th quadrant​

Answer 1

Answer:

HERE'S YOUR ANSWER IN THE PHOTO

Answer 2

Answer:

3√5+2√7/12

Step-by-step explanation:

we know sinalpha=2/3 and cosbeta=3/4.

put sin alpha in a triangle:

means put 2 on perpendicular and 3 on hypotenuse.and using Pythagoras theorm we find that base =√5.

so from this triangle, cosalpha=base /hypotenuse=√5/3.

similarly, apply on cosbeta. and make a triangle put the values. and by Pythagoras theorm:

perpendicular =√7 and sin beta=√7/4.

so value of cos(alpha-beta)=

we know that cos(A-B)=cosAcosB-sinAsinB

cos(alpha-beta) =√5/3*3/4+2/3*√7/4

=√5/4+√7/2*3=√5/4+√7/6=3√5+2√7/12.