Respuesta :

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If we want to write the given four numbers in another form, we can write it like this;

[tex]tan45=sin45/cos45=1[/tex]

[tex]sin30=sin(\frac{\pi }{2}-60 )=cos60=\frac{1}{2}[/tex]

[tex]cot45=cos45/sin45=1[/tex]

[tex]sec60=1/cos60=\frac{1}{1/2} =2[/tex]

Now let's rewrite the given expression and get the result.

[tex](tan45.sin30)-(cot45/sec60)=(1.\frac{1}{2})-(\frac{1}{2} )=0[/tex]

Itz5151

Answer:

0

Step-by-step explanation:

Using trigonometric functions and table to substitute values,we obtain

  • [tex]1 \times \sin45 - \cfrac{ \cot(45) }{ \sec(60) } [/tex]

  • [tex] \sin(30) - \cfrac{ \cfrac{\cos(45)}{ \sin45} }{ \cfrac{1}{ \cos(60) } } [/tex]

  • [tex] \cfrac{1}{2} - \cfrac{ \cfrac{\cos(45)}{ \sin45} }{ \cfrac{1}{ \cos(60) } } [/tex]

Rewrite 1/cos(60) as

  • [tex] \cfrac{1}{2} - \cfrac{ \cos(45) \times \cos(60) }{ \sin(45) } [/tex]

Rewriting again:

  • [tex] \cfrac{1}{2} - \cfrac{ \cancel{\cfrac{\sqrt{2}}{2} }\times \cfrac{1}{2} }{ \cancel{\cfrac{ \sqrt{2} }{2}} } [/tex]

  • [tex] \cfrac{1}{2} - \cfrac{1}{2} [/tex]

[LCM of 2 is 2]

  • [tex] \cfrac{1 - 1}{2} = \boxed0[/tex]

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