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

Trignometry

Cool goIITian

Joined:	9 Oct 2007
Post:	73

9 Oct 2007 01:00:22 IST

0 People liked this

297

Solve for the range of y........

None

If y= (sin^4 x -cos^4 x +sin^2 x cos^2x )/(sin^4 x+ cos^4 x +sin^2 x cos^2 x)

and x

(0, 90degrees)

Share this article on:

Comments (1)

Gaurav |spideyunlimited| Ragtah

Moderator

Joined: 16 Dec 2006

Posts: 3373

11 Oct 2007 16:13:39 IST

Like 0 people liked this

sin⁴x - cos⁴x + sin²x.cos²x /   sin⁴x + cos⁴x + sin²x.cos²x

= (sin²x - cos²x) + sin²x.cos²x    /    (sin²x + cos²x)² - sin²x.cos²x

= sin²x - cos²x + sin²x.cos²x   /     1 - sin²x.cos²x

= sin²x - cos²x ( 1 - sin²x) / sin²x + cos²x - sin²x.cos²x

= sin²x - cos⁴x   /   sin²x + cos⁴x

now the max and min values of this expression depends on cos⁴x .. as first quadrant is under consideration... if cos x is maximum then value of expression will be minimum and vice versa.

Thus min value is -1 when cos x = 1
and max value is +1 when cosx = 0 ( minimum possible value in 1st quadrant)

thus range of y is [0,1]

*PLZ RATE*

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