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Hannah_Ahn

  • 2 years ago

prove the identity \[\left( \cos x \over 1 +\sin x \right)=\left( 1-\sin x \over \cos x \right)\]

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  1. Yifan12879
    • 2 years ago
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    LHS/RHS=1

  2. Yifan12879
    • 2 years ago
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    because cos x cos x = 1- sin x sin x

  3. Mr.Math
    • 2 years ago
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    By multiplying the left hand side by 1-sinx, we get \[{\cos{x}(1-\sin{x}) \over 1-\sin^2{x}}={\cos(x)(1-\sin(x) \over \cos^2(x)}={1-\sin{x} \over \cos{x}}\]

  4. Mr.Math
    • 2 years ago
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    Which is what we have on the right hand side obviously.

  5. Hannah_Ahn
    • 2 years ago
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    that was simple. thanks.

  6. Mr.Math
    • 2 years ago
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    It is simple! :)

  7. Hannah_Ahn
    • 2 years ago
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    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

  8. Mr.Math
    • 2 years ago
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    His argument is not that difficult, he's using that if a=b\(\ne\)0, then a/b=1.

  9. Yifan12879
    • 2 years ago
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    actually i should use LHS-RHS=0 to prove that

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