Respuesta :

fieryanswererft

Formula's:

  • [tex]\rm cot = \dfrac{cos}{sin}[/tex]
  • [tex]\rm sec = \dfrac{1}{cos}[/tex]

solve:

[tex]\rightarrow \rm sin \ cot \ sec = 1[/tex]

[tex]\rightarrow \rm sin \ \dfrac{cos}{sin} \ \dfrac{1}{cos} = 1[/tex]

[tex]\rightarrow \rm \dfrac{sin \ cos}{sin \ cos} = 1[/tex]

[tex]1 = 1[/tex]

L.H.S = R.H.S

Hence both sides are equal and confirmed true. identify proved.

semsee45

Answer:

Prove  [tex]sin(x)cot(x)sec(x)=1[/tex]

Using the following trig identities:

[tex]cot(x)=\dfrac{1}{tan(x)}[/tex]

[tex]sec(x)=\dfrac{1}{cos(x)}[/tex]

[tex]\dfrac{sin(x)}{cos(x)}=tan(x)[/tex]

[tex]\implies sin(x)cot(x)sec(x)=sin(x) \cdot \dfrac{1}{tan(x)} \cdot\dfrac{1}{cos(x)}[/tex]

                                    [tex]= \dfrac{1}{tan(x)} \cdot\dfrac{sin(x)}{cos(x)}[/tex]

                                    [tex]= \dfrac{1}{tan(x)} \cdot tan(x)[/tex]

                                    [tex]= \dfrac{tan(x)}{tan(x)}[/tex]

                                    [tex]=1[/tex]

Hence [tex]sin(x)cot(x)sec(x)=1[/tex]

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