anonymous
  • anonymous
prove the identity \[\left( \cos x \over 1 +\sin x \right)=\left( 1-\sin x \over \cos x \right)\]
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
LHS/RHS=1
anonymous
  • anonymous
because cos x cos x = 1- sin x sin x
Mr.Math
  • Mr.Math
By multiplying the left hand side by 1-sinx, we get \[{\cos{x}(1-\sin{x}) \over 1-\sin^2{x}}={\cos(x)(1-\sin(x) \over \cos^2(x)}={1-\sin{x} \over \cos{x}}\]

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Mr.Math
  • Mr.Math
Which is what we have on the right hand side obviously.
anonymous
  • anonymous
that was simple. thanks.
Mr.Math
  • Mr.Math
It is simple! :)
anonymous
  • anonymous
Yifan you help me so much! and I really appreciate it, but many of times I don't understand the way you teach.. I am sorry. :S
Mr.Math
  • Mr.Math
His argument is not that difficult, he's using that if a=b\(\ne\)0, then a/b=1.
anonymous
  • anonymous
actually i should use LHS-RHS=0 to prove that

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