Question

Prove that ( secA-cosecA). (tanA+cotA+1)=$\frac{sec³-cosec³}{secA.cosecA}$

HELP

Answer 1

(1/cosA-1/sinA)(sinA/cosA+cosA/sinA+1)
=(sinA/cosAsinA-cosA/cosAsinA)(sin²A/sinAcosA+cos²A/sinAcosA+sinAcosA/sinAcosA)
=sin³A/cos²Asin²A-cos³A/cos²Asin²A
converting in terms of sec and cosec:
1/cosec³A-1/sec³A×[reciprocating the denominator]sec²Acosec²A
=sec³A/sec³Acosec³A-cosec³A/sec³Acosec³A × sec²Acosec²A    {cancelling}
=sec³A-cosec³A÷sec²Acosec²A = RHS.....Proved (to understand better...copy this working in a sheet of paper).....Nice question!