Show the identity can be derived from a sum or a difference identity and the pythagorean identity?

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Show the identity can be derived from a sum or a difference identity and the pythagorean identity?

$cos (2 a) = 1 - 2 {sin}^{2} a$ $cos(2a)=1-2sin^2a$

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Answer 1 · 2018-06-03T18:50:14

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Explanation:

Remember the angle sum identity

$cos (x + y) = cos (x) cos (y) - sin (x) sin (y)$ $color(blue)(cos(x+y)=cos(x)cos(y)-sin(x)sin(y)$

Now let $x = y = a$ $color(red)(x=y=a$

$cos (a + a) = cos (a) cos (a) - sin (a) sin (a)$ $cos(a+a)=cos(a)cos(a)-sin(a)sin(a)$

$\Rightarrow cos (2 a) = {cos}^{2} (a) - {sin}^{2} (a)$ $=>cos(2a)=cos^2(a)-sin^2(a)$

By the pythagorean trig identity ${cos}^{2} (a) = 1 - {sin}^{2} (a)$ $color(blue)(cos^2(a)=1-sin^2(a)$

$cos (2 a) = (1 - {sin}^{2} (a)) - {sin}^{2} (a)$ $cos(2a)=(1-sin^2(a))-sin^2(a)$

$\Rightarrow cos (2 a) = 1 - 2 {sin}^{2} (a) \leftarrow What we wanted to show$ $=>cos(2a)=1-2sin^2(a) larr color(red)"What we wanted to show"$

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Math

Humanities

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Show the identity can be derived from a sum or a difference identity and the pythagorean identity?

$cos (2 a) = 1 - 2 {sin}^{2} a$ $cos(2a)=1-2sin^2a$

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

Show the identity can be derived from a sum or a difference identity and the pythagorean identity?

cos(2a)=1-2sin^2acos(2a)=1−2sin2acos(2a)=1-2sin^2a

1 Answer

Explanation:

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$cos (2 a) = 1 - 2 {sin}^{2} a$ $cos(2a)=1-2sin^2a$