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Trignometry

Blazing goIITian

 Joined: 30 Nov 2009 Post: 333
10 Feb 2010 20:05:40 IST
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GET 10 HATS!!!!!!!!! SOLVE THIS QUESTION ND I WILL SHOWER YOU WITH HATS!
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

FIND THE VALUE OF        tan(pi/16) + 2 tan(pi/8)  +  4

the ans is cot pi/16

but please don't back explain assuming cot pi/16 to be the value!

Scorching goIITian

Joined: 9 Nov 2008
Posts: 271
10 Feb 2010 22:10:32 IST
4 people liked this

It's quite tough to write those trigonometrical equations here, so I'll just copy prewritten tags:                                                                   tan pi/16 = sin (pi/16) / cos (pi/16)

Now, using half angle formulae, we know that cos pi/16 =  ==

Similarly,sin pi/16= =  =

Thus,  = = (after some simple rationalization.

We know=

Thus, tan(pi/16) + 2 tan(pi/8)  +  4 = , which is simply 1/(tan pi/16) = cot pi /16 Hence, the value is found.

Blazing goIITian

Joined: 30 Nov 2009
Posts: 333
11 Feb 2010 11:56:58 IST
1 people liked this

ya i agree but is there a better solution?

Blazing goIITian

Joined: 30 Nov 2009
Posts: 333
18 Feb 2010 15:05:28 IST
1 people liked this

got a better soln since all the options were

in the form of cot(pi/16)+x where x is a constan

let us assume cot(pi/16)+x to be the sum of given expresion

cotk-tank=2*cot2k (u can prove it easily)

tan(pi/16) + 2 tan(pi/8)  +  4 tan(pi/4) = cot(pi/16)+x

x+cot[pi/16] - tan[pi/16] = 2cot[2pi/16]+x

2cot[2pi/16] - 2tan[pi/]8 =4cot[pi4]

4cot[pi4] - 4 tan[pi/4]=0

therefore sum is cot[pi/16]

isn't it simper?

P?::::::::::P?:::::::::::::::::::P?::::::::::::::::::::::::::::::P?::::::::::::

Blazing goIITian

Joined: 30 Nov 2009
Posts: 333
20 Feb 2010 23:46:44 IST
0 people liked this

thanks for the hat!

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