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Trignometry

Cool goIITian

Joined:	22 Mar 2008
Post:	88

4 Apr 2008 14:40:19 IST

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317

Trigonometry question-very confusing

None

tan 165/2 degree =(root 3+ root 2) (root 2 +1)

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arpan1

Blazing goIITian

Joined: 15 Mar 2008

Posts: 684

4 Apr 2008 14:55:44 IST

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here is one method

165/2 = 45 + 150/4

apply tan on both sides

u get

tan 165/2 = (1+ tan 150/4) / (1- tan 150/4)

now from here there can be 2 approaches

method 1

tan 150 = tan (75 + 75)

use tan (a+b) =( tan a + tanb )/ 1 - tan a. tanb

u get tan 75= ( 4 -

3 )

again find tan (37.5) as done above and substitute in the first eqn.

method -2

this method is more of verification rather than proof and is useful in solving mcq

tan 165/2 = (1+ tan 150/4) / (1- tan 150/4)

after u get upto this, apply C and D

and check with the ans ....

rate me, if satisfied

anchit saini

Blazing goIITian

Joined: 1 Feb 2008

Posts: 1251

4 Apr 2008 15:30:55 IST

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tan 165 = tan 2x = - tan 15 = 2 tan x / ( 1 - tan ^2 x)

also

putting the value and taking tan x = x , we get the quadratic in x as --

(1-

now

the positive value of x comes out to be (as tan 165/2 is positive) --

[-(

now on rationalising the denominator and solving further we get the final equation as -->

x =

6 +

2 + 2 +

3

=

6 + 2 +

2 +

3

=

2) + 1(

2 +

3)

=

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