fishinggirl22
fishinggirl22
13-05-2022
Mathematics
contestada
Simplify (sinx + cosx) ^2/ sin2x
Respuesta :
Hrishii
Hrishii
13-05-2022
[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]
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