Question
Download Solution PDFSimplify the following.
\(\frac{\sin^3 α + \cos^3 α}{\sin α + \cos α}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
\(\frac{\sin^3 α + \cos^3 α}{\sin α + \cos α}\)
Formula Used:
a3 + b3 = (a + b) (a2 + b2 - ab)
sin2θ + cos2θ = 1
Calculation:
\(\frac{\sin^3 α + \cos^3 α}{\sin α + \cos α}\) = [(sin α + cos α) (sin2α + cos2α - sinα cosα)]/(sin α + cos α)
⇒ 1 - sin α cos α
The value is 1 - sin α cos α.
Last updated on Jul 15, 2025
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