Question

Prove That , Cos2x = 2Cos²x - 1​

Answer 1

Answer:

refer to attachment ☺️☺️☺️☺️

Answer 2

$\underline{ \large{ \bold{Identity :- \: }}}$

$\to\bold{Cos( \: A \: + \: B \: )} = \bold{Cos \: A \: \: \times Cos \: B \: \: - \: Sin \: A \: \: \times \: Sin \: B \: \: } \\ \\ \to \bold{ {Sin }^{2}x = 1 - {Cos }^{2}x }$

$\large{\underline{ \bold{ To \: Prove :- \: }}}$

$\to \bold{Cos2x \: = \: \bold{2 {Cos}^{2}x - 1}}</p><p>$

$\large{ \underline{ \bold{Proof :- \: }}}$

$\to\bold{Cos2x \: } \\ \to\bold{Cos( \: x \: + \: x \: )} \\ \to\bold{Cosx \: \times Cosx \: - \: Sinx \: \times \: Sinx } \\ \to\bold{ {Cos}^{2}x \: - \: {Sin}^{2}x } \\ \to \bold{{Cos}^{2}x \: - ( \: 1 - {Cos }^{2} \: ) } \\ \to \bold{{Cos }^{2} \: - 1 + {Cos }^{2} } \\ \to \bold{2{Cos }^{2}x - 1}</p><p></p><p>$