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Question
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
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Solution
`= 1/(cosectheta-cottheta)xx (cosectheta+cottheta)/(cosectheta+cottheta)-1/sintheta`
`= (cosectheta+cottheta)/(cosec^2theta-cot^2theta) - 1/sintheta`
`cosectheta+cottheta - 1/sintheta`
`1/sintheta+costheta/sintheta - 1/sintheta`
`1/sintheta+(costheta-1)/sinthetaxx(costheta+1)/(costheta+1)`
`1/sintheta+(cos^2theta-1)/((1+costheta)sintheta)`
`1/sintheta-(1-cos^2theta)/(sintheta(1+costheta))`
`1/sintheta - (sin2theta)/(sintheta(1+costheta))`
`1/sintheta-sintheta/(1+costheta)`
`1/sintheta - (sintheta/sintheta)/(1/sintheta+costheta/sintheta)`
`1/sintheta-1/(cosectheta+cottheta)`= RHS
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