# Does the equation sin^2x - cos^2x = 3 have any solution.

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### 2 Answers

The solution of `sin^2x - cos^2x = 3` has to be determined.

`sin^2x - cos^2x = 3`

=> `cos^2x - sin^2x = -3`

=> `cos 2x = -3`

But the range of the cosine function is [-1, 1], `cos 2x = -3` is not true for any value of x.

**The equation `sin^2x - cos^2x = 3` does not have a solution.**

We have to find a value of x that satisfies `sin^2x - cos^2x = 3`

Use the relation `sin^2x + cos^2x = 1` or `cos^2x = 1 - sin^2x`

`sin^2x - cos^2x = 3`

`sin^2x - 1 + sin^2x = 3`

`2*sin^2x = 4`

`sin^2x = 2`

`sin x = +- sqrt 2`

But the value of sin x is in the set [-1, 1] and `+-sqrt 2` does not lie in this set.

The equation `sin^2x - cos^2x = 3` does not have a solution.