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

1 Answer
George C.
Sep 2, 2016

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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