prove that sin+cos/sin-cos +sin-cos/sin+cos=2/1-2cos2
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(sin + cos)^2 + ( sin - cos)^2 )/ sin^2 - cos^2
2 sin^2 + 2 cos^2 )/ 1 - cos^2 - cos^2
2( sin^2 + cos^2)/ 1 - 2 cos^2
2/ ( 1- 2 cos^2)
2 sin^2 + 2 cos^2 )/ 1 - cos^2 - cos^2
2( sin^2 + cos^2)/ 1 - 2 cos^2
2/ ( 1- 2 cos^2)
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