anonymous
  • anonymous
is cos^2x(1+tan^2x)=1 an identity? explain your reasoning.
Mathematics
schrodinger
  • schrodinger
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johnweldon1993
  • johnweldon1993
I would say so \[\large cos^2(x)(1 + tan^2(x)) = 1\] What is \(\large 1 + tan^2(x)\) ?
anonymous
  • anonymous
\[\sec^2 x\]
johnweldon1993
  • johnweldon1993
Right...so \[\large cos^2(x)sec^2(x) = 1\] Now...we know \(\large sec^2(x)\) can be written as \(\large \frac{1}{cos^2(x)}\) So \[\large cos^2(x)(\frac{1}{cos^2(x)}) = 1\] \[\large \frac{cos^2(x)}{cos^2(x)} = 1\] Is that a true statement?

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anonymous
  • anonymous
yes, thank you!

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