Question

if sinA=15/53 and sinB=33/65,find values of sin(A+B) and sin(A-B)

Answer 1

sinA=15/53 and sinB=33/65
From here we can find cos A and cos B
cosA = √1-sin²A = √1-(15/53)² = √2584/2809
cosB = √1-sin²B = √1-(33/65)² = √3136/4225



Sin(A+B) = sinACosB + CosA SinB
= 15/53 × √3136/4225 + √2584/2809×33/65


Now sin(A-B) = sinAcosB - cosAsinB
=> 15/53 × √3136/4225 -√2584/2809×33/65

Answer 2

sin(A+B)=sinAcosB+cosAsinB
Sin(A-B) =sinAcosB-cosAsinB
apply this formula
hint is in place of cosA and cosB u just put this value cosA=√1-sin²A
and cosB=√1-sin²B
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