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Cos^3a-sin^3a/cosa-sina

User Scott Drew
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1 Answer

3 votes

Answer:

1 + cosa sina

Explanation:


(cos^3a-sin^3a)/(cosa-sina)

cos³a - sin³a ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

cos³a - sin³a

= (cosa - sina )(cos²a + cosa sina + sin²a)

= (cosa - sina)(1 + cosa sina) [ sin²a + cos²a = 1 ]

Then


(cos^3a-sin^3a)/(cosa-sina)

=
((cosa-sina)(1+cosasina))/(cosa-sina) ← cancel (cosa - sina) on numerator/ denominator

= 1 + cosa sina

User Tomas Tintera
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