Question

what is the value of cot7 1/2 degree? without using calculator !

Answer 1

cot x = 1 / tan x

use your calculator to find tan 7.5 degrees and plug this into the above

Answer 2

well i have some options

Answer 3

a) sq root 6+ sq r 2 + sq r 3 + sq r 4
b) sq r 6 + sq r 2 - sq r 3 - sq r 4
c) sq r 6 -sqr 2- sq r 3- sqr 4
d sq r 6 + sq r 2 - sq r 3- sqr 4

Answer 4

is that cot(7.5)? @kritima @cwrw238 the question says you can't use a calculator =/

Answer 5

yeh it is cot 7.5

Answer 6

I don't see how you would do this without a calculator though lol.

Answer 7

i know that tan 7.5 degree is ( sq r 3- sq r 2)/ ( sq r 2 - 1 )

Answer 8

so to find cot(7.5) then that's just 1/tan(7.5). Since you know what tan(7.5) is, to get 1/tan(7.5), just flip the fraction and you'll have the answer. @kritima

Answer 9

i did that but i didn't get the answer !

Answer 10

my answer isn't in the option

Answer 11

Oh that's because you didn't rationalise the denominator. So here is what you need to do. We know the following information:\[\bf \tan(7.5)=\frac{\sqrt{3}-\sqrt{2}}{\sqrt2-1}\]Now to find cot(7.5), we just plug that in:\[\bf \cot(7.5)=\frac{1}{\tan(7.5)}=\frac{ \sqrt2-1 }{ \sqrt3-\sqrt2 }\]Now we must rationalise the denominator, i.e. we must eliminate the roots in the denominator. We do this by multiplying both the numerator and denominator of the fraction by the conjugate. The conjugate is \(\bf \sqrt{3}+\sqrt{2}\), as you see we just changed the minus to a plus.\[\bf \frac{ \sqrt2-1 }{ \sqrt3-\sqrt2 }=\frac{ (\sqrt2-1)(\sqrt3+\sqrt2) }{ (\sqrt3-\sqrt2)(\sqrt3+\sqrt2) }=\frac{\sqrt{6}+\sqrt4-\sqrt{3}-\sqrt2}{1}\]Can you tell me what the answer will be now? @kritima

Answer 12

cot(7.5) is 1/tan(7.5) then 7.5 is the half-angle of 15...which in turn is the half angle of 30. so it's a bunch of half-angle formulas. i assume that's what you did?

Answer 13

i also got the same @genius12

Answer 14

@kritima I think the choices are typed up wrong?

Answer 15

but if you use half angle formula over here then you'll get completly different answer !

Answer 16

@kritima forget that, I'm saying that perhaps the choices are typed up wrong because I'm pretty confident that's the right answer.

Answer 17

i aslo thought so @genius12

Answer 18

but when you use half angle formula you'll get one which is in option

Answer 19

so i m bit confused which is the right answer

Answer 20

@kritima I see what the problem is now. The given value of tan(7.5) is incorrect. Are you that is what is given?

Answer 21

@genius12 sadly, the answer you're confident in does not match a calculator's answer. you may not use a calculator in answering, but you may use it in checking after all

Answer 22

@abb50 I was assuming that the given value of tan(7.5) is correct, which is the one @kritima gave me. Turns out the value he gave me was wrong which is why the answer is wrong.

Answer 23

although, one of the choices matches the calculator's answer

Answer 24

ok i made mistake the value of tan 7.5 i gave you was wrong @ genius12 . i m sorry !

Answer 25

tan(7.5) is sqrt 2 + 1 not minus..

Answer 26

now i got it all right . the answer is option a

Answer 27

yeh you are right @abb50

Answer 28

@kritima why did you give me the wrong value, u said sqrt(2) - 1 lol...

Answer 29

actully i made a mistake. and i was also assuming the same sorry ! @genius12

Answer 30

its ok :)

Answer 31

and thank you all of you !