Question

Sin 8a, cos 6a, tg 4a

Answer 1

Sin8a=2sin4a•cos4a; cos6a=cos^2(3a)-sin^2(3a); tg4a=2tg2a/1-tg^2(2a)

Answer 2

Sure, I can help you with trigonometric expressions for sin(8a), cos(6a), and tan(4a).

1. sin(8a): To calculate sin(8a), we can use the double angle formula for sine:

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sin(2x) = 2 * sin(x) * cos(x)

Let x = 4a, so we have:

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sin(8a) = sin(2 * 4a) = 2 * sin(4a) * cos(4a)

Now, let's use another double angle formula:

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sin(2x) = 2 * sin(x) * cos(x)

to find sin(4a):

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sin(4a) = sin(2 * 2a) = 2 * sin(2a) * cos(2a)

And one more time, using half-angle formula:

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cos(2x) = cos^2(x) - sin^2(x)

to find cos(2a):

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cos(2a) = cos^2(a) - sin^2(a)

Now we have all the necessary values:

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sin(4a) = 2 * sin(2a) * cos(2a)
cos(2a) = cos^2(a) - sin^2(a)
sin(8a) = 2 * sin(4a) * cos(4a)

2. cos(6a): To calculate cos(6a), we can use the triple angle formula for cosine:

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cos(3x) = 4 * cos^3(x) - 3 * cos(x)

Let x = 2a, so we have:

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cos(6a) = cos(3 * 2a) = 4 * cos^3(2a) - 3 * cos(2a)

And we already know cos(2a) from the previous calculations.

3. tan(4a): To calculate tan(4a), we can use the tangent double angle formula:

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tan(2x) = (2 * tan(x)) / (1 - tan^2(x))

Let x = 2a, so we have:

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tan(4a) = tan(2 * 2a) = (2 * tan(2a)) / (1 - tan^2(2a))

Now you have the trigonometric expressions for sin(8a), cos(6a), and tan(4a) in terms of a, using the previously calculated values.