prove that tan A/secA-1 +tan A/sec A+1=2 cosec A
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tanA / secA - 1 + tanA / secA + 1
= sinA/cosA / 1/ cosA - 1 + sinA/cosA / 1/cosA + 1
on simplifying
sinA / 1 - cosA + sinA / 1 + cosA
=sinA + sinA.cosA + sinA - sinA.cosA / 1 - cos A
=2sinA / sin A
=2 / sinA
=2cosecA
= sinA/cosA / 1/ cosA - 1 + sinA/cosA / 1/cosA + 1
on simplifying
sinA / 1 - cosA + sinA / 1 + cosA
=sinA + sinA.cosA + sinA - sinA.cosA / 1 - cos A
=2sinA / sin A
=2 / sinA
=2cosecA
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