Sum and Difference Identities for Sine and Tangent

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Sum and Difference Identities for Sine and Tangent
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So now we want an identity for the sine of the
sum of two angles.
Lets use some identities we already know to
figure out this identity. First well use a
cofunction identity.
distribute the negative and regroup (associative
property)
use cosine difference identity
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Now well use a cofunction identities again.
Sum and Difference Identities for Sine
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You will need to memorize these two as well. Say
them as you use them and you will get them
memorized.
Sum of angles for sine is, "Sine of the first,
cosine of the second plus cosine of the first
sine of the second." You can remember that
difference is the same formula but with a
negative sign.
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A little harder because of radians but ask, "What
angles on the unit circle can I add or subtract
to get negative pi over 12?" hint 12 is the
common denominator between 3 and 4.
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You will need to know these formulas so let's
study them a minute to see the best way to
memorize them.
opposite
cos has same trig functions in first term and in
last term, but opposite signs between terms.
same
sin has opposite trig functions in each term but
same signs between terms.
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There are also sum and difference formulas for
tangent that come from taking the formulas for
sine and dividing them by formulas for cosine and
simplifying (since tangent is sine over cosine).