Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

Trig (answer included) need explanation?

I may be overthinking this but what happened to cos15-cos45 and sin(5pi/24) x Sin(pi/24)

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  • DWRead
    Lv 7
    4 weeks ago

    Difference formula for sine:

    sin(α-β) = sinα·cosβ-cos·αsinβ

    Sum formula for cosine:

    cos(α+β) = cosα·cosβ-sinα·sinβ

  • sin(45)cos(15) - cos(45)sin(15) = 

    sin(45 - 15) = 

    sin(30) = 

    1/2cos(5pi/24)cos(pi/24) - sin(5pi/24)sin(pi/24) = cos(5pi/24 + pi/24) =

    cos(6pi/24) =

    cos(pi/4) =

    sqrt(2)/2

    A + B = 1/2 + sqrt(2)/2 = (1 + sqrt(2)) / 2

    sin(x + y) = sin(x)cos(y) + sin(y)cos(x)

    sin(x - y) = sin(x)cos(y) - sin(y)cos(x)

    cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

    cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

    You need to learn the trig identities.  You seem to think that cos(a + b) = cos(a)cos(b), or something similar.  That's just wrong.

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