tanq-cotq=2sin2q-1/sinqcosq
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= tanq - cotq
= (sinq/cosq) - (cosq/sinq)
= (sin2q - cos2q)/(sinq*cosq)
= -(cos2q-sin2q)/(sinq*cosq) [here, minus is taken common]
= -(1-2sin2q)/(sinq*cosq) [since, cos2q-sin2q = 2cos2q-1 = 1-2sin2q ]
= now multiply minus inside
= (2sin2q-1)/(sinq*cosq)
= (sinq/cosq) - (cosq/sinq)
= (sin2q - cos2q)/(sinq*cosq)
= -(cos2q-sin2q)/(sinq*cosq) [here, minus is taken common]
= -(1-2sin2q)/(sinq*cosq) [since, cos2q-sin2q = 2cos2q-1 = 1-2sin2q ]
= now multiply minus inside
= (2sin2q-1)/(sinq*cosq)
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