Use identities (no calculators) to fi nd the exact value for (sin 9)(sin 36)-(cos 9)(cos 36)

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Use identities (no calculators) to fi nd the exact value for (sin 9)(sin 36)-(cos 9)(cos 36)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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9+36 =?
how can you play with those angles to get an angle for which there is an exact value
does this equals cos 45?

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Other answers:

yes
which is 1/ sqrt(2)
\[\sin \theta = \cos 90 - \theta\]
How do I figure out if its positive of negative
sines, cosines and tangents in the first quadrant (0-90 degrees) are all positive
i've just checked my maths formula book and the given expression = -cos(9 + 36) not cos (9+36) so the correct answer is -(1/sqrt2)
this is not the formula for \[cos(a+b)\] but it is its negative.
of course 9+36=36+9=45
but the formula for \[cos(a+b)=cos(a)cos(b)-sin(a)sin(b)\]
and \[sin(a)sin(b)-cos(a)cos(b)=-(cos(a)cos(b)-sin(a)sin(b)\] that is why you had to change the sign from \[\frac{\sqrt{2}}{2}\]to \[-\frac{\sqrt{2}}{2}\]

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