Question

Prove that: $WiredFaculty$

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Solution

space space sinA. space sin left parenthesis 60 degree minus straight A right parenthesis. space sin left parenthesis 60 degree plus straight A right parenthesis

WiredFaculty

left square bracket because space sin space left parenthesis straight A plus straight B right parenthesis space sin left parenthesis straight A minus straight B right parenthesis space equals space sin squared straight A space minus space sin squared straight B right square bracket

WiredFaculty

equals space sinA over 4 open square brackets 3 minus 4 sin squared straight A close square brackets space equals space 1 fourth left square bracket 3 sinA space minus space 4 sin cubed straight A right square bracket space equals space 1 fourth sin 3 straight A

Hence,

space space sinA. space sin left parenthesis 60 degree minus straight A right parenthesis. space sin left parenthesis 60 degree plus straight A right parenthesis space equals space 1 fourth space sin 3 straight A

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