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(tan theta)/(1-cot theta)+cot theta...

(tan theta)/(1-cot theta)+cot theta

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Prove that: ((tan theta)/(1-tan theta))-((cot theta)/(1-cot theta))=(cos theta+sin theta)/(cos theta-sin theta)

If (tan theta)/(tan theta- tan 3 theta)=1/3 find the value of (cot theta)/(cot theta- cot 3 theta)

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Let theta in (0,pi/4) and t_1=(tan theta)^(tan theta), t_2=(tan theta)^(cot theta), t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta), then