wampominater
  • wampominater
Verify the identity. quantity one minus sine of x divided by cosine of x equals cosine of x divided by quantity one plus sine of x
Mathematics
katieb
  • katieb
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wampominater
  • wampominater
looks like this \[\frac{ 1 - sinx }{ cosx } = \frac{ cosx }{ 1 + sinx }\]
Nnesha
  • Nnesha
cross multiply ?
Nnesha
  • Nnesha
or i would solve right to make it equal

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Nnesha
  • Nnesha
right side*
wampominater
  • wampominater
ok. so how would I start with right side?
Nnesha
  • Nnesha
you need to multiply denominator and numerator by the conjugate of 1+sinx
wampominater
  • wampominater
ahh ok
wampominater
  • wampominater
so it is \[\frac{ cosx - sinxcosx }{ 1-\sin^2x}\]
Nnesha
  • Nnesha
okay so you don't need to distribute 1-sinx by cosx at the numerator \[\frac{ \cos(x)(1-\sin(x)) }{ 1-\sin^2 }\] apply the identity 1-sin^2x equal to what ?
wampominater
  • wampominater
cos^2x
wampominater
  • wampominater
so it would be \[\frac{ cosx(1-sinx) }{ \cos^2x }\]
Nnesha
  • Nnesha
yes right cos^2x can be written as cos x times cos x \[\huge\rm \frac{ \cos(x)(1-\sin(x)) }{ cos(x) \times cos(x) }\]
wampominater
  • wampominater
so factor out top and bottom leaves me with \[\frac{ 1-sinx }{ cosx }\]
Nnesha
  • Nnesha
yep
wampominater
  • wampominater
and thats it
wampominater
  • wampominater
ty!
Nnesha
  • Nnesha
yep
Nnesha
  • Nnesha
my pleasure!

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