## Hannah_Ahn Group Title prove the identity $\left( \cos x \over 1 +\sin x \right)=\left( 1-\sin x \over \cos x \right)$ 2 years ago 2 years ago

1. Yifan12879

LHS/RHS=1

2. Yifan12879

because cos x cos x = 1- sin x sin x

3. Mr.Math

By multiplying the left hand side by 1-sinx, we get ${\cos{x}(1-\sin{x}) \over 1-\sin^2{x}}={\cos(x)(1-\sin(x) \over \cos^2(x)}={1-\sin{x} \over \cos{x}}$

4. Mr.Math

Which is what we have on the right hand side obviously.

5. Hannah_Ahn

that was simple. thanks.

6. Mr.Math

It is simple! :)

7. Hannah_Ahn

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

His argument is not that difficult, he's using that if a=b$$\ne$$0, then a/b=1.

9. Yifan12879

actually i should use LHS-RHS=0 to prove that