Home » Ask & Discuss » Mathematics. » Trignometry « Back to Discussion

Trignometry

Blazing goIITian

Joined:	9 Feb 2007
Post:	1347

20 Feb 2007 14:34:02 IST

0 People liked this

693

trigonometry

None

the number of all possible triplets (a1,a2,a3) such that

a1 + a2 (cos 2x ) + a3 sin²x = 0 for all x is ;;

a. zero b. one

c. three d.infinte

Share this article on:

Comments (8)

vishak p

Blazing goIITian

Joined: 9 Feb 2007

Posts: 1347

20 Feb 2007 14:48:42 IST

Like 0 people liked this

???

vinu

Blazing goIITian

Joined: 15 Dec 2006

Posts: 321

20 Feb 2007 14:52:31 IST

Like 0 people liked this

Hi vish0001,

given is........a₁+a₂(1-2sin²x)+a₃sin²x=0;

a₁+a₂=sin²x(2a₂-a₃) ;

If the above eq shud be satisfied

x , u shud 've (2a₂-a₃) = 0;

i.e; 2a₂=a_{3 ;}a₁= - a₂;

a₁:a₂:a₃= -1:1:2 ;

So, u can've infinite values for (a₁,a₂,a₃).

vishak p

Blazing goIITian

Joined: 9 Feb 2007

Posts: 1347

20 Feb 2007 14:56:28 IST

Like 0 people liked this

i am not able to understand why 2a2-a3 should be equal to 0 ??

vishak p

Blazing goIITian

Joined: 9 Feb 2007

Posts: 1347

20 Feb 2007 14:57:47 IST

Like 0 people liked this

also , vinu can u please answer the other questions asked by me in the expert level by me ?? please i am dying for answers !

Ramya Hegde

Blazing goIITian

Joined: 8 Feb 2007

Posts: 612

20 Feb 2007 16:02:50 IST

Like 1 people liked this

for the given condition to be true for all x, the coefficients must be zero, so in that case, whatever may be the value of x, u always get the LHS as zero, i.e. to get LHS as identity, u need a₁=-a₂ and 2a₂=a₃.

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

21 Feb 2007 14:45:16 IST

Like 2 people liked this

a₁ + a₂cos2x + a₃sin²x = 0

=> a₁ + a₂(1-2sin²x) + a₃sin²x = 0

=> (a₁ + a₂) + (a₃ - 2a₂)sin²x = 0

Since its independent of x then coefficient of sin²x is 0.

i.e. (a₃ - 2a₂) = 0

and (a₁ + a₂) = 0

=> a₁:a₂:a₃ = (-1):1:2

Hence infinite triplets are possible.

vishak p

Blazing goIITian

Joined: 9 Feb 2007

Posts: 1347

21 Feb 2007 16:30:14 IST

Like 0 people liked this

sir, why has the coefficient of sin square x being written down as 0 ? i mean we can do thi type of arrangement only in vectors, complex numbers but not in algebra ! please explain!

CyBorG

Forum Expert

Joined: 6 Jan 2007

Posts: 706

21 Feb 2007 18:41:16 IST

Like 1 people liked this

See Vish when the co-efficient of sin(square)x is zero whatever may be the value of x the equation will be true.

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team