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

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Answer 1 · 2018-03-03T14:35:19

$1/csc^(2⁡)x +1/sec^(2)x =1$

$1/(1/sin^(2⁡)x )+1/(1/cos^(2⁡)x )=1$

$sin^2⁡x+cos^2⁡x=1$

$1=1$

Use reciprocal identity to transform $1/csc^2 x$ and $1/sec^2 x$ to $1/[1/ (sin^2 x)]$ and $1/[1/(cos^2 x)]$ respectively.
Reciprocate $sin^2 x$ and $1/(cos^2 x)$ you will get $sin^2x$ and $cos^2 x$ , respectively.
$sin^2⁡x+cos^2⁡x$ is equal to $1$ by the Pythagorean Fundamental Identity.

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