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3 years ago

Derive this identity from the sum and difference formulas for cosine:

Mathematics

1 answer:

DiKsa [7]3 years ago

4 0

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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2 years ago

Find the distance between the points given. (-3, 2) and (9, -3) A √37 B √61 C 13

Kitty [74]

Answer:

$\huge{ \fbox{ \sf{13 \: units}}}$

Option C is correct.

Step-by-step explanation:

$\star{ \sf{ \: Let \: the \: points \: be \: a \: and \: b}}$

$\star{ \sf{ \: let \: A(-3, 2) \: be \: (x1 \:, y1) \: and \: B(9, -3) \: be \: (x2 \:, y2) }}$

$\underline{ \sf{Finding \: the \: distance \: between \: the \: given \: points}} :$

$\boxed{ \sf{Distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}$

$\mapsto{ \sf{ \sqrt{ {(9 - ( - 3))}^{2} + {( - 3 - 2)}^{2} } }}$

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$\mapsto{ \sf{ \sqrt{ {(12)}^{2} + {( - 5)}^{2} } }}$

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$\mapsto{ \sf{ \sqrt{ {(13)}^{2} } }}$

$\mapsto{ \sf{ 13 \: units}}$

Hope I helped!

Best regards! :D

~ $\text{TheAnimeGirl}$

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