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lisov135 [29]
3 years ago
11

___ cosb =1/2 sin(a+b)+sin(a-b)?

Mathematics
2 answers:
vodomira [7]3 years ago
8 0

Answer:

That would be sina.

Step-by-step explanation:

sin(a+b) = sinacosb + cosasinb

sin(a-b) = sinacosb -  cosasinb

Adding we get  sin(a+b) + sin(a-b) = 2sinaccosb

so sinacosb = 1/2sin(a+b) + sin(a-b)

dem82 [27]3 years ago
6 0

Answer:

sina

Step-by-step explanation:

We have

          sin(a+b) = sina cosb + cosa sinb ---------------------eqn 1

           sin(a-b) = sina cosb - cosa sinb ---------------------eqn 2

eqn 1 + eqn 2

          sin(a+b) + sin(a-b) = sina cosb + cosa sinb + sina cosb - cosa sinb

          sin(a+b) + sin(a-b) = 2sina cosb

          sina\times cosb =\frac{1}{2}(sin(a+b) + sin(a-b))

So answer is sina

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