Question

1-cos x÷sinx + sinx÷1-cosx=2÷sinx

Answer 1

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$\sf{\dfrac{1-cos(x)}{sen(x)}+\dfrac{sen(x)}{1-cos(x)}=\dfrac{(1-cos(x))\cdot(1-cos(x))+sen^2(x)}{sen(x)\cdot(1-cos(x))}}\\\sf{\dfrac{1-2cos(x)+cos^2(x)+sen^2(x)}{sen(x)\cdot(1-cos(x))}}\\\sf{\dfrac{1-2cos(x)+1}{sen(x)\cdot(1-cos(x))}}\\\sf{\dfrac{2-2cos(x)}{sen(x)\cdot(1-cos(x))}}\\\sf{\dfrac{2\cdot\diagdown\!\!\!\!\!\!(1-\diagdown\!\!\!\!\!\!cos(x))}{sen(x)\cdot\diagdown\!\!\!\!\!\!(1-\diagdown\!\!\!\!\!\!cos(x))}}=\boxed{\boxed{\boxed{\boxed{\sf{\dfrac{2}{sen(x)}}}}}}$