Question #ffc58
2 Answers
Explanation:
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)cos(A+B)=cosAcosB-sinAsinB#
#•color(white)(x)sin(A-B)=sinAcosB-cosAsinB#
#•color(white)(x)cos2A=cos^2A-sin^2A#
#"consider left hand side"#
#sinx(cosxcosy-sinxsiny)-cosx(sinxcosy-cosxsiny)#
#=cancel(sinxcosxcosy)-sin^2xsinycancel(-sinxcosxcosy)+cos^2xsiny#
#=siny(cos^2x-sin^2x)#
#=sinycos2x=" right hand side "rArr" proved"#
We have:
Let's apply the compound angle identities for
Then, let's apply the double angle identity for