How do you verify the identity $(cos^2theta-sin^2theta)=(cottheta-tantheta)/(tantheta+cottheta)$ ?

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How do you verify the identity $(cos^2theta-sin^2theta)=(cottheta-tantheta)/(tantheta+cottheta)$ ?

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Answer 1 · 2016-09-02T19:06:09

See explanation...

Explanation:

Use:

$sin^2 theta + cos^2 theta = 1$

$tan theta = sin theta / cos theta$

$cot theta = cos theta / sin theta$

Hence:

$cos^2 theta - sin^2 theta = (cos^2 theta - sin^2 theta)/(sin^2 theta + cos^2 theta)$

$color(white)(cos^2 theta - sin^2 theta) = ((cos^2 theta - sin^2 theta) -: (cos theta sin theta))/((sin^2 theta + cos^2 theta) -: (cos theta sin theta))$

$color(white)(cos^2 theta - sin^2 theta) = (cos theta / sin theta - sin theta / cos theta)/(sin theta/cos theta + cos theta/sin theta)$

$color(white)(cos^2 theta - sin^2 theta) = (cot theta - tan theta)/(tan theta + cot theta)$

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How do you verify the identity $(cos^2theta-sin^2theta)=(cottheta-tantheta)/(tantheta+cottheta)$ ?

1 Answer

Explanation:

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How do you verify the identity (cos^2theta-sin^2theta)=(cottheta-tantheta)/(tantheta+cottheta)(cos^2theta-sin^2theta)=(cottheta-tantheta)/(tantheta+cottheta)?

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Explanation:

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How do you verify the identity $(cos^2theta-sin^2theta)=(cottheta-tantheta)/(tantheta+cottheta)$ ?