( sintheta -cosectheta ) ( cost theta - sectheta )= 1/ tantheta + cot theta
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first break the bracket
sine theta (cos theta - sec theta) - cosec theta ( cos theta - sec theta)
=sin ×cos - sin× sec - cos ×cosec - cosec× sec
= sin × cos - sin / cos - cos /sin + 1/ sin×cos sin×cos - tan - cot + 1/ sin × cos = 2 cot
sin × cos + 1/sin × cos = 2 cot + cot + tan
sin× cos + 1/sin × cos = 3 cot + tan
(sin^2 + cos^2)+1/sin×cos= 3cot + tan
1+1/ sin × cos= 3 cot + tan
2/ sin × cos = 3 cot + tan
sine theta (cos theta - sec theta) - cosec theta ( cos theta - sec theta)
=sin ×cos - sin× sec - cos ×cosec - cosec× sec
= sin × cos - sin / cos - cos /sin + 1/ sin×cos sin×cos - tan - cot + 1/ sin × cos = 2 cot
sin × cos + 1/sin × cos = 2 cot + cot + tan
sin× cos + 1/sin × cos = 3 cot + tan
(sin^2 + cos^2)+1/sin×cos= 3cot + tan
1+1/ sin × cos= 3 cot + tan
2/ sin × cos = 3 cot + tan
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