Question
Verify the Identity.$$\sin ^{3} t+\cos ^{3} t=(1-\sin t \cos t)(\sin t+\cos t)$$
Step 1
We can rewrite this using the identity $a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$ where $a=\sin t$ and $b=\cos t$. So, $\sin ^{3} t+\cos ^{3} t=(\sin t+\cos t)(\sin^{2} t-\sin t \cos t+\cos^{2} t)$. Show more…
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