Question

Demuestra la siguiente identidad

Answer 1

Respuesta:

Explicación paso a paso:

$\sqrt{\dfrac{1-cos\beta}{1+cos\beta}}+\sqrt{\dfrac{1+cos\beta}{1-cos\beta}}=2csc\beta\\\\\\\sqrt{\dfrac{1-cos\beta}{1+cos\beta}\times\dfrac{1+cos\beta}{1+cos\beta} }+\sqrt{\dfrac{1+cos\beta}{1-cos\beta}\times\dfrac{1-cos\beta}{1-cos\beta}}=2csc\beta\\\\\\\sqrt{\dfrac{(1-cos\beta)(1+cos\beta)}{(1+cos\beta)(1+cos\beta)}}+\sqrt{\dfrac{(1+cos\beta)(1-cos\beta)}{(1-cos\beta))(1-cos\beta)}}=2csc\beta\\\\\\\sqrt{\dfrac{1-cos^2\beta}{(1+cos\beta)^2}}+\sqrt{\dfrac{1-cos^2\beta}{(1-cos\beta)^2}}=2csc\beta$

$\sqrt{\dfrac{sen^2\beta}{(1+cos\beta)^2}}+\sqrt{\dfrac{sen^2\beta}{(1-cos\beta)^2}}=2csc\beta\\\\\\\dfrac{sen\beta}{1+cos\beta}+\dfrac{sen\beta}{1-cos\beta}=2csc\beta\\\\\\\dfrac{sen\beta(1-cos\beta+1+cos\beta)}{(1+cos\beta)(1-cos\beta)}=2csc\beta\\\\\\\dfrac{sen\beta(2)}{1-cos^2\beta}=2csc\beta\\\\\\\dfrac{2sen\beta}{sen^2\beta}=2csc\beta\\\\\\\dfrac{2}{sen\beta}=2csc\beta\\\\\\\boxed{2csc\beta=2csc\beta}$

Answer 2

Respuesta:

Explicación paso a paso: