# Using Trigonometric Identities

• Jan 20th 2013, 01:44 PM
vaironxxrd
Using Trigonometric Identities
Hello Everyone,

I have the following instruction, "Use trigonometric identities to transform one side of the equation into the other" ?

First I don't exactly understand what the instructions are saying.

The problem is as follows

cos Θ sec Θ = 1

The book gives me the solution which is

cos Θ sec Θ = 1 $\displaystyle \frac{1}{sec Θ}$ = 1

( 0 < Θ < π/2) (I guess this means Θ is an acute angle)
• Jan 20th 2013, 02:58 PM
Plato
Re: Using Trigonometric Identities
Quote:

Originally Posted by vaironxxrd
I have the following instruction, "Use trigonometric identities to transform one side of the equation into the other" ? First I don't exactly understand what the instructions are saying. The problem is as follows
cos Θ sec Θ = 1
The book gives me the solution which is
cos Θ sec Θ = 1 $\displaystyle \frac{1}{sec Θ}$ = 1
( 0 < Θ < π/2) (I guess this means Θ is an acute angle)

If the question is to solve for $\displaystyle \theta$ in the equation $\displaystyle \cos(\theta)\sec(\theta)=1$ then the answer given makes no sense.
Because the solution is $\displaystyle \forall\theta\left[\theta\ne\frac{(2n+1)\pi}{2}\right]$.

On the other hand, did the statement begin with restrictions on $\displaystyle \theta~?$
• Jan 20th 2013, 03:42 PM
vaironxxrd
Re: Using Trigonometric Identities
Quote:

Originally Posted by Plato
If the question is to solve for $\displaystyle \theta$ in the equation $\displaystyle \cos(\theta)\sec(\theta)=1$ then the answer given makes no sense.
Because the solution is $\displaystyle \forall\theta\left[\theta\ne\frac{(2n+1)\pi}{2}\right]$.

On the other hand, did the statement begin with restrictions on $\displaystyle \theta~?$

The book first gives the instruction, "transform one side of the equation into the other" (Which doesn't make any sense to me)
It also doesn't provide any specific angle it just states the following $\displaystyle ( 0 < \theta < \pi/2)$

The actual problem to be solved is...
$\displaystyle cos \theta sec \theta = 1$

The solution is...
"Simplify the expression on the left-hand side of the equation until you obtain the right side"
$\displaystyle cos\theta sec\theta$ = $\displaystyle \frac{1}{sec\theta}\cdot sec\theta$ = 1
• Jan 20th 2013, 04:17 PM
Plato
Re: Using Trigonometric Identities
Quote:

Originally Posted by vaironxxrd
The book first gives the instruction, "transform one side of the equation into the other" (Which doesn't make any sense to me)
It also doesn't provide any specific angle it just states the following $\displaystyle ( 0 < \theta < \pi/2)$

The actual problem to be solved is...
$\displaystyle cos \theta sec \theta = 1$

The solution is...
"Simplify the expression on the left-hand side of the equation until you obtain the right side"
$\displaystyle cos\theta sec\theta$ = $\displaystyle \frac{1}{sec(\theta})\cdot sec\theta$ = 1

It is absolutely true that if $\displaystyle 0<\theta<\frac{\pi}{2}$ then $\displaystyle \cos(\theta)\sec(\theta)=1$.

So what is the big deal?
• Jan 20th 2013, 04:36 PM
vaironxxrd
Re: Using Trigonometric Identities
Quote:

Originally Posted by Plato
It is absolutely true that if $\displaystyle 0<\theta<\frac{\pi}{2}$ then $\displaystyle \cos(\theta)\sec(\theta)=1$.