Question #b8b69

2 Answers
Rajat Chatterjee · Alan P.
Nov 2, 2016

yes,for #x=pi/4,sin^2x+cos^2x=2sinxcosx#

Explanation:

here for# x=pi/4,sinx=cosx=(1/sqrt2)#
so ,#sinx=cosx#
#sinx-cosx=0#
squaring both sides we get#(sinx-cosx)^2=0#
or ,#sin^2x+cos^2x-2sinxcosx=0#
or#sin^2x+cos^2x=2sinxcosx# proved.

Alan P.
Nov 5, 2016

While this relation is true for certain values of #x# it is not valid in general.
I can not be proven as an identity because it is not, in general, true.

Explanation:

#sin^2(x)+cos^2(x)=1# (this is an extension of the Pythagorean Theorem)

For x=0
#color(white)("XXX")2sin(x)⋅cos(x)=2×0×1=0#

#sin^2(x)+cos^2(x)≠2sin(x)⋅cos(x)#

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