fishinggirl22 fishinggirl22

13-05-2022
Mathematics

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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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