Question 924109
How do you prove the identity by choosing one side to solve: cot^2(x)+sec^2(x)=tan^2(x)+csc^2(x)?
<pre><font face = "Tohoma" size = 4 color = "indigo"><b>cot<sup>2</sup> x + sec<sup>2</sup> x = tan<sup>2</sup> x + csc<sup>2</sup> x</pre>
<u>Left-side:</u><pre>{{{cot^2 (x) + sec^2 (x)}}}
{{{cot^2 (x) + tan^2 (x) + 1}}} ------ {{{sec^2 (x) = tan^2 (x) + 1}}}
{{{tan^2 (x) + cot^2 (x) + 1}}} ------ Rearranging
{{{tan^2 (x) + cot^2 (x) + 1}}}
{{{tan^2 (x) + csc^2 (x)}}} ---------- {{{cot^2 (x) + 1 = csc^2 (x)}}}
Thus, the LEFT SIDE is PROVEN as being equal to RIGHT-SIDE</font face = "Tohoma" size = 4 color = "indigo"> </b>