(cosec A - Sin A) (sec A - cos A) (Tan A + cotton A) =1
Answers
Answered by
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.
: )
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.
: )
Similar questions