1.

Prove that (sin+cos)2 + (sin- cos)2 = 2​

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Answer:

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Step-by-step EXPLANATION:

(sinx−cosx)2+(sinx+cosx)2=2

sin2x−2sinxcosx+cos2x+sin2x+2sinxcosx+cos2x=2

TERMS EQUAL 1

from the PYTHAGOREAN theorem

also, blue terms equal 1

So

1−2sinxcosx+1+2sinxcosx=2

green terms together equal 0

So now you have

1+1=2

2=2


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