Prove the identity:
(cosec A – sin A ) (sec A – cos A) (tan A + cot A) = 1
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LHS =(tanA+cotA)(cosecA-SinA)(secA-CosA)
tanA+cotA=(SinA/CosA)+(CosA/SinA)
= (sin²Α+cos²Α)/cosAsinA
= 1/cosAsinA
CosecA-SinA=(1/SinA)-SinA
= (1-sin²Α)/SinA= cos²Α/sinA
SecA-cosA=(1/cosA)-cosA=(1-cos²Α)/cos A
=sin²Α/cosA
(tanA+cotA)(cosecA-SinA)(secA-cosA)
=(1/sinAcosA)(cos²Α/SinA)(sin²Α/CosA)
=1=RHS
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