Question

if a+b=45 then prove that (cota-1)(cotb-1)=2

Answer 1

hy

Answer 2

hey

Answer 3

did u know

Answer 4

,cotacotb-1/cota+cotb=1
cota+cotb=cotacotb-1
cotacotb-cota-cotb=2.

Answer 5

there's basically the answer fill in the rest by yourself.

Answer 6

hy

Answer 7

hy math

Answer 8

a+b =45 ---> a = b = 45-a
\[cot a =\frac{1}{tan a}\]
so we can re write like \[(\frac{1}{tana}-1)*(\frac{1}{tan(45-a)}-1)\]
now, make the same denominator for the terms inside the bracket
\[(\frac{1-tana}{tana})*(\frac{1-tan(45-a)}{tan(45-a)})\]

Answer 9

moreover, \[tan(45-a) = \frac{tan45-tana}{1+tan45tana}\] and tan45=1
replace into this we have\[ tan (45 -a) = \frac{1-tana}{1+tana}\]
now plug the whole thing into the form
we have

Answer 10

sorry , near answer but I have to go, will be back to finish, or someone else can continue my work.

Answer 11

hy

Answer 12

you are the asker? ok, i am back, too late but if you still need it. I can continue.

Answer 13

hy 66

Answer 14

yes

Answer 15

u can continue

Answer 16

I see many smarties here, let them contribute,ok?

Answer 17

ok

Answer 18

Could you first show us what you've done with the question please?

Answer 19

hy please help me

Answer 20

@bijay56 Are you there? It's pointless for us to help you if you don't even attempt the question. It's for your benefit. We're not gaining anything if we just do the question for you.

Answer 21

question-if a+b=45 then prove that (cota-1)(cotb-1)=2

Answer 22

Could you show what you've done please?

Answer 23

ans-cot(a+b)=cot45

Answer 24

or,cotb.cota-1/cotb+cota=1

Answer 25

Those are just the answers. I want you to show me your working out.

Answer 26

or,cotb.cota-1=cotb+cota

Answer 27

now what to do

Answer 28

Have you attempted the question yet?

Answer 29

yes

Answer 30

i think u wont help me

Answer 31

hy 66

Answer 32

hy mertsj

Answer 33

Mertsj, why it take that long, you " are typing replies" in 11 minutes!!!???

Answer 34

bijay56, if you've attempted the question, could we at least have a look at what you've done so far?

Answer 35

this is a new comer for sure. he/she even not know how to tag people. poor guy!!

Answer 36

No point us helping you if you don't show us what you've done. Showing us what you've done is an important aspect of showing us that you want to learn and understand what we're trying to do for you.

Answer 37

@Azteck tolerate, he is off line, we come up with the problem on many ways, it's hard for the asker follow.

Answer 38

Then we just have to wait until he/she comes back online. Then we can start helping the person.

Answer 39

you see, he said "hy 66" "hy 56" . he is poor.

Answer 40

If a+b=45 then b = 45-a
\[(\cot (a)-1)(\cot (45-a)-1)=2\]
\[(\frac{1}{\tan (a)}-1)(\frac{1}{\tan (45-a)}-1)=2\]
\[(\frac{1}{\tan a}-1)(\frac{1+\tan 45\tan a}{\tan 45-\tan a}-1)=2\]
\[(\frac{1}{\tan a}-1)(\frac{1+\tan a}{1-\tan a}-1)=2\]
\[(\frac{1-\tan a}{\tan a})(\frac{1+\tan a-(1-\tan a)}{1-\tan a})=2\]
\[(\frac{1}{\tan a})(\frac{2\tan a}{1})=2\]
\[2=2\]

Answer 41

and Mertsj, I guess you are kicked out the net. cannot take that long to reply

Answer 42

thanks Mertsj, don't delete, to the poor guy, definitely he will be back to take it.

Answer 43

can go to sleep now. bye bye everybody. hehehe

Answer 44

a+b=45,
=>cot(a+b)=cot45
=>(cota + cotb)/(cotacotb-1)=1
=>cota + cotb=cotacotb-1
=>cotacotb -cota -cotb -1=0
=>cotacotb -cota -cotb +1 = 2
=>(cota-1)(cotb-1)=2