Question #65e09

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Answer 1 · 2017-07-05T15:20:08

You can use trigonometric identities and simplify.

Here are two trigonometric identities that are needed in this problem:

$sin(a+b) = sin a cos b + cos a sin b$
$cos(a-b) = cos a cos b + sin a sin b$

We can rewrite the problem based on these identities.

$sin(y+π/2)+cos(y-π)=0$

$sin y cos (π/2) + cos y sin (π/2) + cos y cos (π) + sin y sin (π) = 0$

![http://www.softschools.com/math/trigonometry/unit_circle_charts/]( useruploads.socratic.org )

Using the unit circle, we can simplify.

$sin y * color(red)0 + cos y * color(red)1 + cos y * color(red)(-1) + sin y * color(red)0 = 0$

$cos y - cos y = 0$

$0 = 0$