watkenses
watkenses watkenses
  • 24-01-2022
  • Mathematics
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Prove [tex]\:\frac{cos\theta }{sec\theta }+\frac{sin\theta }{csc\theta }=1[/tex]

Respuesta :

jimrgrant1 jimrgrant1
  • 24-01-2022

Answer:

see explanation

Step-by-step explanation:

Using the identities

sec x = [tex]\frac{1}{cosx} [/tex]  ,  csc x = [tex]\frac{1}{sinx} [/tex]

sin²x + cos²x = 1

Consider the left side

[tex]\frac{cos0}{sec0} [/tex] + [tex]\frac{sin0}{csc0} [/tex]

= [tex]\frac{cos0}{\frac{1}{cos0} } [/tex] + [tex]\frac{sin0}{\frac{1}{sin0} } [/tex]

= cos²Θ + sin²Θ

= 1 = right side , thus proven

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