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Assoli18 [71]
3 years ago
5

Proof: sin(x) + cos(x) = √2sin(x + π/4)

Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
5 0
Hello : 
sin(x) + cos(x) = √2(1/√2 sin(x) +1/√2 cos(x))
but : 1/√2 = cos(π/4) =   sin(<span> π/4)
</span>sin(x) + cos(x) = √2( cos(π/4)sin(x) + sin( π/4) cos(x)) =√2<span>sin(x + π/4)
</span>because : cos(π/4)sin(x) + sin( π/4) cos(x)=sin(x + π/4) by identity :
sin(a+b) = sina cosb +cosa sinb
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