Prove: \frac{tanA }{1-cot A} + \frac{cotA}{1-tanA} = 1+ tanA + cotA
mysticd:
It is not clear , plz , explain where is / symbol
TanA/1-cotA + cotA/1-tanA
It's the LHS
Is it clea or should I post another question?
It's ok. Wait
Answers
Answered by
2
Hi
LHS = tanA/(1-cotA ) + cotA/(1-tanA)
= [tanA/(1-1/tanA)]+[(1/tanA)/(1-tanA)]
= [tan² A/(tanA-1)]-[1/tanA(tanA-1 )]
=[ 1/(tanA-1) ][ tan²A - 1/tanA ]
= [ 1/(tanA - 1 ) ][ (tan³ A - 1³ )/tanA ]
= [ (tanA-1)[tan²A+1×tanA + 1²]/[(tanA-1) tanA]
=( tan² A + tanA + 1 )/ tanA
= ( tan² A/tanA ) + ( tanA/tanA)+1/tanA
= tanA + 1 + cotA
= 1 + tanA + cotA
= RHS
Hence proved .
I hope this helps you.
: )
LHS = tanA/(1-cotA ) + cotA/(1-tanA)
= [tanA/(1-1/tanA)]+[(1/tanA)/(1-tanA)]
= [tan² A/(tanA-1)]-[1/tanA(tanA-1 )]
=[ 1/(tanA-1) ][ tan²A - 1/tanA ]
= [ 1/(tanA - 1 ) ][ (tan³ A - 1³ )/tanA ]
= [ (tanA-1)[tan²A+1×tanA + 1²]/[(tanA-1) tanA]
=( tan² A + tanA + 1 )/ tanA
= ( tan² A/tanA ) + ( tanA/tanA)+1/tanA
= tanA + 1 + cotA
= 1 + tanA + cotA
= RHS
Hence proved .
I hope this helps you.
: )
Oh, wow. Thank you so much for the help!
Answered by
1
Hey.....!!!! :)) ✌️✌️
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Q. Prove: \frac{tanA }{1-cot A} + \frac{cotA}{1-tanA} = 1+ tanA + cotA
Solution:-
=> tanA / (1-1/tanA)+(1/tanA)/(1-tanA)
=> tan2A / (tanA-1)+1 / (tanA(1-tanA))
=> (1 / (1-tanA)) ((1 / tanA)-tan2A)
=> (1 / (1-tanA)) ((1-tan3A) / tanA)
1-tan3A= (1-tanA) (1+tanA+tan2A) prove it Ans !!
=> 1 / tanA+1+tanA=1+tanA+cotA
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I hope it's help you....!!! :))✌️✌️
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Q. Prove: \frac{tanA }{1-cot A} + \frac{cotA}{1-tanA} = 1+ tanA + cotA
Solution:-
=> tanA / (1-1/tanA)+(1/tanA)/(1-tanA)
=> tan2A / (tanA-1)+1 / (tanA(1-tanA))
=> (1 / (1-tanA)) ((1 / tanA)-tan2A)
=> (1 / (1-tanA)) ((1-tan3A) / tanA)
1-tan3A= (1-tanA) (1+tanA+tan2A) prove it Ans !!
=> 1 / tanA+1+tanA=1+tanA+cotA
========================================
I hope it's help you....!!! :))✌️✌️
Thanks a lot!
my pleasure dear ✌️
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