Question

(cos⁴A-sin⁴A) is equal to​

Answer 1

$\huge\star{\mathfrak{\underline{\red{Answer}}}}$

$\large{\sf{\underline{\underline{Step \: by \: step \: explanation:-}}}}$

$\large\leadsto\tt\ Cos^4A \: - \: Sin^4A \\ \\ \large\leadsto\tt\ (Cos^2A)^2 \: - \: (Sin^2A)^2$

Using identity ;

$\tt\ (a+b) (a-b)\: = \: a^2 \: - \: b^2$

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$\large\leadsto\tt\ (Cos^2A \: + \: Sin^2A)(Cos^2A - Sin^2A)$

According to trigonometric identities;

★$\tt\ Sin^2a \: + \: Cos^2a \: = \: 1$

★$\tt\ Sin^2A \: = \: (1- Cos^2A)$

So;

$\large\leadsto\tt\ (1)(Cos^2A- Sin^2A) \\ \\ \large\leadsto\tt\ Cos^2A \: - ( \: 1-Cos^2A) \\ \\ \large\leadsto\tt\ Cos^2A \: - \: 1 \: + \: Cos^2A \\ \\ \large\leadsto\tt\ 2Cos^2A \: - \: 1$