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### Trig Equation

```
Date: 6/22/96 at 9:54:16
From: Igor Srdanovic
Subject: Trig. Equation

Hi!

I have a math problem. It's an equation. Hope you can solve it.

(cos(x))^2+(sin(x))^2=(15*(cos(x))^2)/18)-(1/2)

x=?
```

```
Date: 6/22/96 at 11:8:49
From: Doctor Anthony
Subject: Re: Trig. Equation

As you have written the equation, the left hand side will equal 1.
The equation then can be written:

(15/18)cos^2(x) - 1/2 = 1

(5/6)cos^2(x) = 3/2

cos^2(x) = 18/10

cos^2(x) = 1.8

cos(x) = sqrt(1.8) = 1.34164

There can be no real solution to this equation since
-1 < or = cos(x) < or = 1 for real x. I have some doubts about the
equation you have written down, particularly as the left hand side
immediately simplifies to 1.  Perhaps you can check it and post a
correction if necessary.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Trigonometry

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