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KengaRu [80]
3 years ago
15

Prove. sin³A-cos³A/sinA-cosA = 1+sinAcosA​

Mathematics
1 answer:
katovenus [111]3 years ago
7 0

Answer:

\frac{ \sin {}^{3} A -  \cos {}^{3}  A }{ \sin A -  \cos A}  \\  \\ { \sf{ =  \frac{ {( \sin A -  \cos A)}^{3}   +  3 \sin A \cos A( \sin A  -   \cos A)}{ \sin A -  \cos A}  }} \\  \\  =  { {( \sin A -  \cos A)}^{2}  +  3 \sin A \cos A} \\ { \sf{ = ( \sin {}^{2}  A +  \cos {}^{2}  A) - 2 \sin  A \cos  A + 3\sin  A \cos  A}}  \\  = { \sf{1 +\sin  A \cos  A }}

#hence proved

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<u><em>Explanation</em></u>

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The first five terms of the arithmetic sequence.

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