Question 205006
Can you please help me thanks alot
Reduce {{{(csc^2x - sec^2x)}}} to an expression containing only {{{tan(x)}}}.
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The two identities we have involving cosecant and secant are

{{{1 + Tan^2phi=sec^2phi}}} and {{{1 + Cot^2phi=csc^2phi}}}

Using them we have

{{{(csc^2x - sec^2x)}}}
{{{1+Cot^2x - (1+Tan^2x)}}}
{{{1+Cot^2x - 1-Tan^2x}}}
{{{Cot^2x-Tan^2x}}}

Now we can get use the identity {{{Cot(phi)=1/Tan(phi)}}} 
to get the term in cotangent in terms of tangent:

{{{1/(Tan^2x)-Tan^2x}}}

That's actually good enough there, but maybe your teacher
wants you to combine those terms:


{{{1/(Tan^2x)-Tan^2x}}}
{{{1/(Tan^2x)-(Tan^2x)/1}}}
{{{1/(Tan^2x)-(Tan^2x)(Tan^2x)/(1(Tan^2x))}}}

{{{1/(Tan^2x)-(Tan^4x)/(Tan^2x)}}}

{{{(1-Tan^4x)/(Tan^2x)}}}

Edwin</pre>