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December 9th, 2015, 10:56 AM   #1
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Please help my homework

I really don't know how to answer this. Please help me.

The question is :
If a and b are 90 or below degrees, and sin a - sin b equals 3/5 and cos a + cos b equals 4/5. How much is sin (a + b).

Thank you
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December 9th, 2015, 02:36 PM   #2
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There's something weird about this question, as specifying "a and b are 90 or below degrees" doesn't help in obtaining the answer. If it were also stated that a and b are positive, there would be no such a and b that satisfy the equations. My guess is that the condition was a failed attempt to ensure that the answer is positive.

If you square and add the given equations, you get 2cos(a)cos(b) - 2sin(a)sin(b) + 2 = 1, so cos(a + b) = -1/2.
It follows that sin(a + b) = ±$\sqrt3/2$. Either sign is possible.
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