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2 years ago

11

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

2 answers:

vodomira [7]2 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]2 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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