Question

Prove That , Cos2x = 1 - Sin²x​

Answer 1

$\underline{ \large{ \bold{Identity :- \: }}} </p><p>$

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

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

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

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

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

Answer 2

Answer:

see explanation

Explanation:

Using  Double angle formula

∙cos2x=cos2x−sin2x

and the identity cos2x=1−sin2x

⇒cos2x=cos2x−sin2x=(1−sin2x)−sin2x

=1−2sin2x= right hand side

hence proved.

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