My Math Forum Determine the values of the variables for which each of the following identities

 Trigonometry Trigonometry Math Forum

 April 23rd, 2018, 03:13 AM #1 Newbie   Joined: Apr 2018 From: East London Posts: 12 Thanks: 0 Determine the values of the variables for which each of the following identities 1.{2x / Cosx- Sinx} = Cosx + Sinx 2.{1 - Sin 2x}/ {Sinx- Cosx} = Sinx - Cosx 3.{Sinx + Sinx} /{1 + Cosx + Cos2x} = Tanx Determine the values of the variables for which each of the following identities are undefined...... Please help i just need get through matric
 April 23rd, 2018, 05:02 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 I'm afraid that doesn't quite make sense. First, an "identity" is an equation that is true for all values of x and so must be defined for all values of x. What you have are not identities but equations. But the word "equation" doesn't make sense here either because it is an "expression", perhaps the left of right side of an equation, that is or is not defined. Finally, I don't know what "matric" means. I thought perhaps "matrix" or "metric" but neither of those has anything to do with this problem. Sine and Cosine themselves are defined for all x. Tan(x) is undefined for x equal to odd multiples of $\displaystyle \frac{\pi}{2}$. Fractions are undefined when the denominator is undefined.
 April 23rd, 2018, 05:35 AM #3 Newbie   Joined: Apr 2018 From: East London Posts: 12 Thanks: 0 Ok I'll see my lecturer today because that's all he gave to us ..Thank you
April 23rd, 2018, 05:43 AM   #4
Math Team

Joined: May 2013
From: The Astral plane

Posts: 1,906
Thanks: 771

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 Originally Posted by Vee88 1.{2x / Cosx- Sinx} = Cosx + Sinx 2.{1 - Sin 2x}/ {Sinx- Cosx} = Sinx - Cosx 3.{Sinx + Sinx} /{1 + Cosx + Cos2x} = Tanx Determine the values of the variables for which each of the following identities are undefined...... Please help i just need get through matric
1. can only be solved numerically.

2. is actually an identity. (Multiply both sides by sin(x) - cos(x).)

-Dan

April 23rd, 2018, 06:56 AM   #5
Senior Member

Joined: Oct 2009

Posts: 608
Thanks: 186

Quote:
 Originally Posted by topsquark 2. is actually an identity. (Multiply both sides by sin(x) - cos(x).)
It is not though. It doesn't hold for $x=\pi/4$.

April 23rd, 2018, 07:07 AM   #6
Math Team

Joined: May 2013
From: The Astral plane

Posts: 1,906
Thanks: 771

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 Originally Posted by Micrm@ss It is not though. It doesn't hold for $x=\pi/4$.
Well, okay, except for values that aren't allowed in the original expression.

Thanks for the catch.

-Dan

April 25th, 2018, 12:59 PM   #7
Senior Member

Joined: Feb 2010

Posts: 697
Thanks: 135

Quote:
 Originally Posted by Vee88 3.{Sinx + Sinx} /{1 + Cosx + Cos2x} = Tanx
$\displaystyle \dfrac{2 \sin x}{1+\cos x +(2\cos^2x-1)}=\tan x$

$\displaystyle \dfrac{2\sin x}{\cos x(2\cos x+1)}=\tan x$

$\displaystyle 2\tan x = \tan x(2\cos x+1)$

$\displaystyle \tan x(2\cos x+1)-2\tan x = 0$

$\displaystyle \tan x(2\cos x-1)=0$. Now you can finish it.

 April 26th, 2018, 01:09 AM #8 Global Moderator   Joined: Dec 2006 Posts: 19,865 Thanks: 1833 Was the first equation intended to be $\displaystyle \frac{\cos 2x}{\cos x - \sin x} = \cos x + \sin x$? That holds except when $x = \pi/4 + \text{k}\pi$, where k is an integer.

 Tags determine, identities, values, variables

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Vee88 Trigonometry 3 April 21st, 2018 02:38 PM Vee88 Trigonometry 3 April 20th, 2018 07:38 AM Sparkleandpop Linear Algebra 1 September 29th, 2015 03:44 AM ka0ttic Computer Science 3 March 17th, 2014 05:08 AM dendimiiii Applied Math 1 February 12th, 2014 09:18 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top