Is it true that since sin2x+cos2x = 1, then sin(x)+cos(x) = 1? Explain your answer.

sin2x+cos2x=1
2sinxcosx+2cos^2x-1=1
2cosx(cosx+sinx-1)=0
2cosx=0 cosx+sinx=1
True

I did this with double angle formulas. sin2x=2sinxcosx, and cos2x=2cos^x-1. With plugging this in, I used factoring. At the end, there are two factors. One of the factors is cosx+sinx-1=0, which is cosx+sinx=1. Therefore, the answer is true.

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lublana lublana · Answer 2 · 2019-07-24T06:57:01+02:00

Answer with Step-by-step explanation:

We are given that it is true since

[tex] sin2x+ cos2x=1[/tex] then[tex] sinx+cosx=1[/tex]

We have to prove that [tex]sinx+cosx=1[/tex]

We know that

[tex] sin2x=2sinxcosx[/tex]

[tex]cos2x=2cos^2x-1[/tex]

Substituting the values then we get

[tex]2sinxcosx+2cos^2x-1=1[/tex]

[tex]2sinxcosx+2cos^2x=1+1[/tex]

[tex]2(sinxcosx+cos^2x)=2[/tex]

[tex]sinxcosx+cos^2x-1=0[/tex]

[tex]cos^2x+sinxcosx=1[/tex]

[tex]cosx(cosx+sinx)=1[/tex]

[tex]cosx=1,cosx+sinx=1[/tex]

Hence, [tex] sinx+cosx=1[/tex]