Tan theta by sec theta minus 1 plus tan theta by sec theta plus 1 is equal to
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tan theta * [ 1/(sec theta -1)+1/(sec theta +1)]
= tan theta * [ 2sec theta/(sec^2 theta -1)]
= tan theta * [ 2sec theta / tan^2 theta ]
= 2sec theta / tan theta
= (2 / cos theta) / (sin theta / cos theta)
= 2 / sin theta
= 2cosec theta
Hope it helps you!
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