# How do you prove  1/sec^2 x + 1/csc^2 x =1?

Mar 3, 2018

 1/csc^(2⁡)x +1/sec^(2)x =1

1/(1/sin^(2⁡)x )+1/(1/cos^(2⁡)x )=1

 sin^2⁡x+cos^2⁡x=1

$1 = 1$

#### Explanation:

1. Use reciprocal identity to transform $\frac{1}{\csc} ^ 2 x$ and $\frac{1}{\sec} ^ 2 x$ to $\frac{1}{\frac{1}{{\sin}^{2} x}}$ and $\frac{1}{\frac{1}{{\cos}^{2} x}}$ respectively.

2. Reciprocate ${\sin}^{2} x$ and $\frac{1}{{\cos}^{2} x}$ you will get ${\sin}^{2} x$ and ${\cos}^{2} x$, respectively.

3. sin^2⁡x+cos^2⁡x is equal to $1$ by the Pythagorean Fundamental Identity.