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Trignometry

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4 Apr 2008 22:30:42 IST

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By componendo and dividendo

None

please verify the following

tan 165/2=(root 3+ root 2) (root 2 +1) by using componendo and dividendo method or by any other method.

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Uday Prakash

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Joined: 7 Dec 2006

Posts: 504

4 Apr 2008 23:42:27 IST

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First find out tan(15/2)

cotA + tanA = 2cosec2A

now use cotA - tanA = 2cot2A

That gives you tanA = cosec2A - cot2A

We can know the value of tan15 using the formula tan(pi/4-A)=[1-tanA]/[1+tanA]

Plugging in those values you get tan15/2 as (3^1/2-2^1/2)(2^1/2-1)

Now we need tan165/2 that's tan(pi-15/2)

That gives the answer to be exactly (3^1/2+2^1/2)(2^1/2+1)

~Cheerio!!!

anchit saini

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5 Apr 2008 00:04:17 IST

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http://www.goiit.com/posts/list/trignometry-trigonometry-question-very-confusing-50959.htm#255934

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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