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Derive this identity from the sum and difference formulas for cosine:
sinasinb=1/2[cos(a-b)cos(a+b)]
Start with the right-hand side since it is more complex.

Derive this identity from the sum and difference formulas for cosine sinasinb12cosabcosab Start with the righthand side since it is more complex class=

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Step-by-step explanation:

½ [cos(a − b) − cos(a + b)]

Using sum and difference formulas:

½ [cos a cos b + sin a sin b − (cos a cos b − sin a sin b)]

Distribute the negative:

½ (cos a cos b + sin a sin b − cos a cos b + sin a sin b)

Combine like terms:

½ (2 sin a sin b)

Simplify:

sin a sin b

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