Verify that sin(A+B) + sin(A-B) = 2sinA sinB ?

2 Answers
Apr 14, 2018

"see explanation"

Explanation:

"using the "color(blue)"addition formulae for sin"

•color(white)(x)sin(A+-B)=sinAcosB+-cosAsinB

rArrsin(A+B)=sinAcosB+cosAsinB

rArrsin(A-B)=sinAcosB-cosAsinB

rArrsin(A+B)+sin(A-B)=2sinAcosB

!=2sinAsinBlarr"check your question"

Apr 14, 2018

It is not an identity.

Explanation:

It is not an identity.

A = 90° , B = 0°
LS: sin(A+B) + sin(A-B) = sin (90°+0°) + sin ( 90°-0°) = 2
RS: 2sinA sinB = 2 sin 90° sin 0° = 2 xx1xx0 = 0
2!=0

= 2sinA sinB

sin(A+B) + sin(A-B) = 2sinA sinB

LHS: sin(A+B) + sin(A-B)

sinAcosB + cosAsinB + sinAcosB - cosAsinB =

sinAcosB + sinAcosB = 2sinAcosB