Answers

2014-05-13T12:41:22+05:30
CotA /1-tanA + tanA /1-cotA
cos^2A /(cosA - sinA)sinA + sin^2A /(sinA - cosA)cosA
(cos^3A - sin^3A) /(cosA - sinA)cosAsinA
(cosA - sinA)(cos^2A + sin^2A + cosAsinA) /(cosA - sinA)cosAsinA
(1 + cosAsinA ) /cosAsinA
cosecAsecA + 1
0
2014-05-13T14:55:00+05:30
CotA/1-tanA+tanA/1-cotA
=[(cosA/sinA)/(1-sinA/cosA)]+[(sinA/cosA)/(1-cosA/sinA)]
=cos^2A/sinA(cosA-sinA)+sin^2A/cosA(sinA-cosA)
=cos^3A-sin^3A/sinAcosA(cosA-sinA)   [a^3-b^3=(a-b)(a^2+b^2+ab)]
=(cosA-sinA)(cos^2A+sin^2A+sinAcosA)/sinAcosA(cosA-sinA)
=1+sinAcosA/sinAcosA           (sin^2A+cos^2A=1)
=(1/sinAcosA)+(sinAcosA/sinAcosA)       (cosecA=1/sinA,secA=1/cosA)
=cosecAsecA+1
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