Question

porfa me ayudan?:(
help me please

Answer 1

Respuesta:

 $P=\sec x.\csc x$          ∨              $P=\cfrac{1}{\cos x. \sin x}$

Explicación paso a paso:

$P=(\tan x+\cfrac{\cos x}{1+\sin x})(\cot x+\cfrac{\sin x}{1+\cos x})\\\\\\P=(\cfrac{\sin x}{\cos x}+\cfrac{\cos x}{1+\sin x})(\cfrac{\cos x}{\sin x}+\cfrac{\sin x}{1+\cos x})\\\\\\P=(\cfrac{\sin x(1+\sin x)+\cos x(\cos x)}{\cos x(1+\sin x)})(\cfrac{\cos x(1+\cos x)+\sin x(\sin x)}{\sin x(1+\cos x)})$

$P=(\cfrac{\sin x+\sin^2x+\cos^2x}{\cos x(1+\sin x)})(\cfrac{\cos x+\cos^2x+\sin^2x}{\sin x(1+\cos x)})\\\\\\P=(\cfrac{\sin x+(\sin^2x+\cos^2x)}{\cos x(1+\sin x)})(\cfrac{\cos x+(\sin^2x+\cos^2x)}{\sin x(1+\cos x)})\\\\\\P=(\cfrac{\sin x+1}{\cos x(1+\sin x)})(\cfrac{\cos x+1}{\sin x(1+\cos x)})\\\\\\P=(\cfrac{(1+\sin x)}{\cos x(1+\sin x)})(\cfrac{(1+\cos x)}{\sin x(1+\cos x)})$

$P=(\cfrac{1}{\cos x})(\cfrac{1}{\sin x})\\\\\\P=\sec x.\csc x$                       ≅                 $P=\cfrac{1}{\cos x. \sin x}$