Answer to Question #347333 in Trigonometry for Stella

Question #347333

If f(x) = sin x, show that f (2x)= 2f(x) f(1/2 π-x).


1
Expert's answer
2022-06-06T23:03:55-0400

If "f(x)=sinx," then

"f(2x)=sin2x=2sinxcosx" (double angle formula).


Let's consider the right side of the equality:

"2f(x)f(\\frac{\\pi}{2}-x)=2sinxsin(\\frac{\\pi}{2}-x)=2sinxcos x,"

because "sin(\\frac{\\pi}{2}-x)=cosx" (co-function identity).


So we have:

"f(2x)=2sinxcosx=2f(x)f(\\frac{\\pi}{2}-x),"

and the statement is proved.


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