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

Question

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

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Thiên Di 1 week 2021-07-21T23:13:05+00:00 2 Answers 1 views 0

Answers ( )

    0
    2021-07-21T23:14:15+00:00

    Answer:

    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

    0
    2021-07-21T23:14:42+00:00

    Answer:

    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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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )