Question

Evaluate Sin^6 – cos^6.

Answer 1

Step-by-step explanation:

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Answer 2

$\Large\underline\mathfrak{Question}$ :-- Evaluate Sin^6A – cos^6A ?

$\Large\bold\star\underline{\underline\textbf{Formula\:used}}$

• (a³-b³) = (a-b)(a²+b²+ab)
• (a³+ b³) = (a+b)(a²+b²-ab)
• (a²-b²) = (a+b)(a-b)
• sin²A + cos²A = 1

$\Large\underline{\underline{\sf{Solution}:}}$

$\sf \: Sin^{6}A - cos^{6}A \\ \\ \red\leadsto \sf \: (sin^{3}A - cos^{3}A)^{2} \\ \\ \red\leadsto \sf \: (sin^{3}A - cos^{3}A)(sin^{3}A + cos^{3}A) \\ \\ \red\leadsto \sf \: [(sinA-cosA)(sin^{2}A+cos^{2}A + sinACosA][(sinA + cosA)(sin^{2}A+cos^{2}A-sinACosA] \\ \\ \red\leadsto \sf \: [(sinA-cosA)(1+sinACosA][(sinA + cosA)(1-sinACosA] \\ \\ \red\leadsto \underline{ \green{\boxed{\sf \: (sin^{2}A - Cos^{2} A)(1 - sin^{2}ACos^{2}A)}}}$

$\rule{200}{4}$