If q=cosec theta - cot theta
Then show that q^2-1/q^2+1 +cos theta=0
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cosec^2x+cot^2x-2cosecx cotx+1/cosec^2x+cot^2x-2cosecx.cotx+1+cosx
1+2cot^2x-2cosec^2x.cosx
2cosec^2x-1-2cosec^2x.cosx
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