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

2 Answers
Jim G.
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"#

mizoo
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 #

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