Mathematics: Prove that: cos^2 (45+A)+cos^2 (45-A)=1

Prove that: cos^2 (45+A)+cos^2 (45-A)=1 - id245245113921041, liln223

Ответ:

nbnb8831

09.08.2021

Mathematics

see explanation

Step-by-step explanation:

Using the cosine addition formula

cos(A ± B ) = cosAcosB ∓ sinAsinB

Then considering the left side

cos²(45 + A) + cos²(45 - A)

= [ cos45cosA - sin45sinA ]² + [cos45cosA + sin45sinA]]²

= [ $\frac{1}{\sqrt{2} }$ cosA - $\frac{1}{\sqrt{2} }$ sinA ]² + [ $\frac{1}{\sqrt{2} }$ cosA + $\frac{1}{\sqrt{2} }$ sinA ]²

= $\frac{1}{2}$ cos²A - sinAcosA + $\frac{1}{2}$ sin²A + $\frac{1}{2}$ cos²A + sinAcosA + $\frac{1}{2}$ sin²A

= cos²A + sin²A

= 1

= right side , then proven

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Ответ:

stphdrn4347

09.08.2021

Mathematics

Step-by-step explanation:

cos 2x=cos²x-sin²x=cos²x-(1-cos²x)=cos²x-1+cos²x=2cos²x-1

2cos²x=1+cos2x

$cos^2x=\frac{1}{2}(1+cos2x)$

cos²(45+A)+cos²(45-A)

$=\frac{1}{2}(1+cos(90+2A))+\frac{1}{2}(1+cos(90-2A))\\=\frac{1}{2} (1-sin2A)+\frac{1}{2} (1+sin 2A)\\=\frac{1}{2} (1-sin2A+1+sin 2A)\\=\frac{1}{2} \times2\\=1$

cos (90-x)=sin x

cos (90+x)=-sin x

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Ответ:

officialrogerfp3gf2s

20.08.2020

Mathematics

43-73 is not 1 it is -30

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Prove that: cos^2 (45+A)+cos^2 (45-A)=1

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Prove that: cos^2 (45+A)+cos^2 (45-A)=1