kayraalessandra kayraalessandra

24-05-2024
Mathematics

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determina [tex]\(\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}=\frac{\sec x}{\sin x}\)[/tex]

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Itz5151 Itz5151

24-05-2024

Step-by-step explanation:

LHS = sinx/cosx + cosx/sinx

Take LCM of sinx and cosx

= (sinx*sinx + cosx*cosx)/sinx*cosx

= sin²x + cos²x/sinx*cosx

sin²x+cos²x = 1

= 1/(sinx*cosx)

1/cos x = secx

= 1/cosx * 1/sinx

= sec/sinx = RHS

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