Question

(codec A - Sin A) ( Sec A - Cos A) (tan A - cot A ) =1
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Answer 1

Explanation-

(cosec A - Sin A) ( Sec A - Cos A) (tan A + cot A ) =1

LHS =(cosecA-SinA)(secA-CosA)(tanA+cotA)

CosecA-SinA=(1/SinA)-SinA

= (1-sin²Α)/SinA= cos²Α/sinA

SecA-cosA=(1/cosA)-cosA=(1-cos²Α)/cos A

=sin²Α/cosA

tanA+cotA=(SinA/CosA)+(CosA/SinA)

= (sin²Α+cos²Α)/cosAsinA

= 1/cosAsinA

so,

(tanA+cotA)(cosecA-SinA)(secA-cosA)

=(1/sinAcosA)(cos²Α/SinA)(sin²Α/CosA)

=1. =RHS. (proved)