How do you verify #(sin(x)+cos(x))^2=1+sin^2(x)#?

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How do you verify #(sin(x)+cos(x))^2=1+sin^2(x)#?

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Answer 1 · 2015-08-04T02:39:30

I think it is not true.

Explanation:

You can write it as:
#sin^2(x)+2sin(x)cos(x)+cos^2(x)=sin^2(x)+cos^2(x)+sin^2(x)#
where you used the fact that:
#1=sin^2(x)+cos^2(x)#
so:
#cancel(sin^2(x))+2sin(x)cos(x)+cancel(cos^2(x))=cancel(sin^2(x))+cancel(cos^2(x))+sin^2(x)#
and:
#2sin(x)cos(x)=sin^2(x)# Not true

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How do you verify #(sin(x)+cos(x))^2=1+sin^2(x)#?

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