Question

Question #b8b69

Answer 1

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.

Answer 2

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)`