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cos - sin +1)/ cos + sin -1
multiply N and D by cos + sin +1
cos - sin +1)( cos + sin +1)/ ( cos + sin -1)( cos + sin +1)
( cos +1)^2 - sin^2)/ cos+ sin)^2 -1
cos^2 +1 + 2cos - sin^2)/ cos^2 + sin^2 + 2cos sin -1
1- sin^2 + 1 + 2cos - sin^2)/ 1+ 2cos sin -1
2 - 2 sin^2 + 2 cos)/ 2cos sin
1 - sin^2 + cos )/ cos sin
cos^2 + cos)/ cos sin
cos ( cos +1)/ cos sin
cos +1)/ sin
cos /sin + 1/sin
cot + cosec
multiply N and D by cos + sin +1
cos - sin +1)( cos + sin +1)/ ( cos + sin -1)( cos + sin +1)
( cos +1)^2 - sin^2)/ cos+ sin)^2 -1
cos^2 +1 + 2cos - sin^2)/ cos^2 + sin^2 + 2cos sin -1
1- sin^2 + 1 + 2cos - sin^2)/ 1+ 2cos sin -1
2 - 2 sin^2 + 2 cos)/ 2cos sin
1 - sin^2 + cos )/ cos sin
cos^2 + cos)/ cos sin
cos ( cos +1)/ cos sin
cos +1)/ sin
cos /sin + 1/sin
cot + cosec
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