Trig identities

  • Thread starter Nelo
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  • #1
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Homework Statement



tan^2x - sin^2x = sin^2x*tan^2x

Homework Equations







The Attempt at a Solution



This is how my teacher solved it.

Sin^2x sin^2x
______ - ______
Cos^2x 1

sin^2x - cos^2x*sin^2x
_________________________
cos^2x

= sin^2x (1-cos^2x)
___________________
cos^2x

=sin^2x *sin^2x
______________
cos^2x


thus giving the answer. I dont understand what happends on the third line. How can 1-cos^2x be bracketed if cos^2x*sin^2x are one term, even though they equal one, how can that equal 1-cos^2x?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
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31
Because in sin2x - cos2xsin2x, sin2x is common in both terms, thus it can be factored as sin2x(1-cos2x).

If you expand the bracket you will get back sin2x - cos2xsin2x, sin2x.
 
  • #3
PeterO
Homework Helper
2,425
46


thus giving the answer. I dont understand what happends on the third line. How can 1-cos^2x be bracketed if cos^2x*sin^2x are one term, even though they equal one, how can that equal 1-cos^2x?


In the third line, what happened was factorisation.
 

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