Question

SinA=8/17,sinB=5/13,prove that sin(A+B) =171/221​

Answer 1

Step-by-step explanation:

we write the answer in the following

given: sinA=8/17

sinB=5/13

to proove:sin(A+B)=171/221

formula :sin(A+B)= sinAcosB+cosAsinB

solution: sinAcosB+cosAsinB

we can find cosA and cosB

from sin²A+cos²A=1

(8/17)²+cos²a=1

64/389-1 = cos²a

cosa= -325/389

cosa= -15/17

from this way we find cos b

cosB= -12/13

sinAcosB+cosAsinB

(8/17)(-12/13)+(-15/17)(5/13)

= from solving this we got

= -100-121/171

=171/221

hence proved

hope it is helps you