How do you verify ${cos}^{2} (x) - {sin}^{2} (x) = 1 - 2 {sin}^{2} (x)$ $cos^2(x)-sin^2(x)=1-2sin^2(x)$ ?

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How do you verify ${cos}^{2} (x) - {sin}^{2} (x) = 1 - 2 {sin}^{2} (x)$ $cos^2(x)-sin^2(x)=1-2sin^2(x)$ ?

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Answer 1 · 2018-06-11T05:37:35

Below

Explanation:

RTP: ${cos}^{2} x - {sin}^{2} x = 1 - 2 {sin}^{2} x$ $cos^2x-sin^2x=1-2sin^2x$

LHS:
${cos}^{2} x - {sin}^{2} x$ $cos^2x-sin^2x$

Recall: ${cos}^{2} x + {sin}^{2} x = 1$ $cos^2x+sin^2x=1$ so ${cos}^{2} x = 1 - {sin}^{2} x$ $cos^2x=1-sin^2x$
= $(1 - {sin}^{2} x) - {sin}^{2} x$ $(1-sin^2x)-sin^2x$

= $1 - {sin}^{2} x - {sin}^{2} x$ $1-sin^2x-sin^2x$

= $1 - 2 {sin}^{2} x$ $1-2sin^2x$

= RHS

Therefore: ${cos}^{2} x - {sin}^{2} x = 1 - 2 {sin}^{2} x$ $cos^2x-sin^2x=1-2sin^2x$

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How do you verify ${cos}^{2} (x) - {sin}^{2} (x) = 1 - 2 {sin}^{2} (x)$ $cos^2(x)-sin^2(x)=1-2sin^2(x)$ ?

1 Answer

Explanation:

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How do you verify cos^2(x)-sin^2(x)=1-2sin^2(x)cos2(x)−sin2(x)=1−2sin2(x)cos^2(x)-sin^2(x)=1-2sin^2(x)?

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Explanation:

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How do you verify ${cos}^{2} (x) - {sin}^{2} (x) = 1 - 2 {sin}^{2} (x)$ $cos^2(x)-sin^2(x)=1-2sin^2(x)$ ?