Use identities (no calculators) to nd the exact value for (sin pi/4)(cos pi/2) + (cos pi/4)(sin pi/2)

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Use identities (no calculators) to nd the exact value for (sin pi/4)(cos pi/2) + (cos pi/4)(sin pi/2)

Mathematics
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this ones the hardest of them all
but if you have a look at it, see what expansion it looks like
and it becomes pretty easy

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Other answers:

this = sin(pi/4 + pi)??
no
sorry pi/2 + pi/4
=sin 3/4 pi = sin 75 degrees
i/m lost now!!
can sin 75 degrees be written in surd form?
its not 75 :|
but sin75 can be written in surd form
no hold om 3/4 pi = 3/4 X 180 = 135 degrees ruyght?
in which case sin 135 = 1 /sqrt 2
you can use sum angles expansion to find exact value of sin75 sin75 = sin(30+45) = sin30cos45+cos30sin45
yes
my brains not working to well today !
Mathematica returns zero after entering the problem expression. The left side of the + sign is zero because Sin[Pi]= zero. Same way for the right side.
It is equal to \(\sin(\frac{\pi}{4}+\frac{\pi}{2})=\sin(3\pi/4)=\sqrt{2}/2\)
(Sin pi/4) was processed as Sin(pi)/4 by Mathematica.
Wolfram may be incorrect but they are reporting that \[\text{Sin}\left[\frac{3 \pi }{4}\right]=\frac{1}{\sqrt{2}}\]

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