What is #sin^2theta-cot^2theta-sectheta # in terms of #costheta#?

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Answer 1 · 2018-05-04T04:52:18

#color(blue)(=> (cos^3 theta - cos^2 theta -cos theta) / (1 - cos^2 theta)#

#sin^2 theta - cot^2 theta - sec theta#

#=> sin^2 theta - cos^2 theta / sin^2 theta - 1 / cos theta#

#=> (sin^4 theta - cos^3 theta - sin^2 theta ) / (sin^2 theta cos theta)#

#=> ((1-cos^2 theta)^2 - cos ^3 theta - (1 - cos^2 theta)) / ((1 - cos^2 theta) * cos theta)#

#=> (cancel1 - 2 cos^2 theta + cos^4 theta - cos^3 theta - cancel1 + cos^2 theta) / (cos theta * (1 - cos^2 theta))#

#=> (cos^4 theta - cos^3 theta - cos^2 theta) / (cos theta * (1 - cos^2 theta))#

#color(blue)(=> (cos^3 theta - cos^2 theta -cos theta) / (1 - cos^2 theta)#