Respuesta :

Hrishii

[tex]\csc 2x+1[/tex]

Step-by-step explanation:

  • [tex]\frac{(\sin x+\cos x)^2}{\sin2x}[/tex]

  • We expand [tex](\sin x+\cos x)^2[/tex] using algebraic identity [tex](a+b)^2=a^2+b^2+2ab[/tex]

  • [tex]=\frac{\sin^2x+\cos^2x+2\sin x.\cos x}{\sin2x}[/tex]

  • [tex]= \frac{1+\sin2x}{\sin2x}[/tex]

  • [tex]=\frac{1}{\sin2x}+\frac{\sin2x}{\sin2x}[/tex]

  • [tex]=\csc 2x+1[/tex]