How do you verify the identify $(1 - sin θ) (1 + sin θ) = {cos}^{2} θ$ $(1-sintheta)(1+sintheta)=cos^2theta$ ?

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How do you verify the identify $(1 - sin θ) (1 + sin θ) = {cos}^{2} θ$ $(1-sintheta)(1+sintheta)=cos^2theta$ ?

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Answer 1 · 2016-08-27T05:41:35

We will use the following well known identities:

${sin}^{2} (θ) + {cos}^{2} (θ) = 1$ $sin^2(theta)+cos^2(theta) = 1$
$a^{2} - b^{2} = (a + b) (a - b)$ $a^2-b^2=(a+b)(a-b)$

With those, starting from the left hand side:

$(1 - sin (θ)) (1 + sin (θ))$ $(1-sin(theta))(1+sin(theta))$

$= 1^{2} - {sin}^{2} (θ)$ $=1^2-sin^2(theta)$

$= ({sin}^{2} (θ) + {cos}^{2} (θ)) - {sin}^{2} (θ)$ $=(sin^2(theta)+cos^2(theta))-sin^2(theta)$

$= {cos}^{2} (θ)$ $=cos^2(theta)$

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How do you verify the identify $(1 - sin θ) (1 + sin θ) = {cos}^{2} θ$ $(1-sintheta)(1+sintheta)=cos^2theta$ ?

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How do you verify the identify (1−sinθ)(1+sinθ)=cos2θ(1-sintheta)(1+sintheta)=cos^2theta?

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How do you verify the identify $(1 - sin θ) (1 + sin θ) = {cos}^{2} θ$ $(1-sintheta)(1+sintheta)=cos^2theta$ ?