Math, asked by raghu556, 1 year ago

(cosec A - Sin A) (sec A - cos A) (Tan A + cotton A) =1

Answers

Answered by mysticd
1
Hi ,

LHS = ( cosecA-sinA)(secA-cosA)(tanA+cotA)

=(cosecA-1/cosecA)(secA-1/secA)(tanA+cotA)

=[cosec²A-1)/cosecA][(sec²A-1)/secA](tanA+cotA)

=[( cot²A)/cosecA][tan²A/secA](tanA+cotA)

= [(cotAtanA)²/cosecAsecA](tanA+cotA)

= ( tanA + cotA )/( cosecAsecA )
[ Since , cotAtanA = 1 ]

= [(sinA/cosA+cosA/sinA)/(cosAsinA)]/cosecAsecA

= [(sin²A+cos²A)/(cosAsinA)]/(cosecAsecA)

= 1/[cosAsinAcosecAsecA]

= 1/(cosAsecA)(sinAcosecA )

= 1

= RHS

I hope this helps you.

: )

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