Question

Nesecuito ayuda con esto esnpara mi tarea porfavor es q no les entiendo
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Answer 1

Respuesta:

b)

$sec(\beta)(1-sen^{2}(\beta ))=cos(\beta )$

c)

$\frac{sen^{2}(\delta)+cos^{2}(\delta) }{tan^{2}(\delta) }=cot^{2}(x)$

d)

$\frac{cot(\theta)}{csc(\theta)}=cos(\theta)$

e)

$sen(\omega)(1+cot^{2}(\omega))= csc(\omega)$

f)

$\frac{sen^{2}(\mu)+cos^{2}(\mu) }{tan^{2}(\mu)+1 }=cos^{2} (\mu)$

g)

$\frac{tan(\sigma)}{sec(\sigma)}=sen(\sigma)$

h)

$(cos(\lambda))(1-cos^{2}(\lambda))=(cos(\lambda))(sen^{2}(\lambda))$

Explicación paso a paso:

Primero hay que saber las identidades trigonométricas:

$sen^{2}(x)+cos^{2} (x)=1\\\\1+cot^{2} (x)=csc^{2}\\\\ tan^{2}(x)+1=sec^{2}(x)\\\\ (x)tan(x)=\frac{sen(x)}{cos(x)}\\\\cot(x)=\frac{cos(x)}{sen(x)}=\frac{1}{tan(x)} \\\\sec(x)=\frac{1}{cos(x)}\\\\csc(x)=\frac{1}{sen(x)}$

b)

$sec(\beta)(1-sen^{2}(\beta ))\\\frac{1}{cos(\beta )}(cos^{2}(\beta))\\\frac{cos^{2}(\beta)}{cos(\beta )}\\cos(\beta )\\\\sec(\beta)(1-sen^{2}(\beta ))=cos(\beta )$

c)

$\frac{sen^{2}(\delta)+cos^{2}(\delta) }{tan^{2}(\delta) }\\\\\frac{1}{tan^{2} (\delta)}\\\\\frac{1}{(\frac{sen(x)}{cos(x)})^{2} }\\\\(\frac{cos(x)}{sen(x)})^{2}\\\\\cot^{2} (x)\\\\\frac{sen^{2}(\delta)+cos^{2}(\delta) }{tan^{2}(\delta) }=cot^{2}(x)$

d)

$\frac{cot(\theta)}{csc(\theta)}\\\\ \frac{\frac{1}{tan(\theta)} }{\frac{1}{sen(\theta)} }\\\\ \frac{sen(\theta)}{tan(\theta)} \\\\ \frac{sen(\theta)}{\frac{sen(\theta)}{cos(\theta)} }\\\\\frac{(sen(\theta))(cos(\theta))}{sen(\theta)}\\\\cos(\theta)\\\\\frac{cot(\theta)}{csc(\theta)}=cos(\theta)$

e)

$(sen(\omega)(1+cot^{2}(\omega))\\(sen(\omega)(csc^{2}(\omega))\\ \\(sen(\omega)(\frac{1}{sen(\omega)} )^{2} \\\\(\frac{sen(\omega)}{sen^{2} (\omega)} )\\\\\frac{1}{sen(\omega) }\\\\csc(\omega)\\\\sen(\omega)(1+cot^{2}(\omega))= csc(\omega)$

f)

$\frac{sen^{2}(\mu)+cos^{2}(\mu) }{tan^{2}(\mu)+1 } \\\\\frac{1}{sec^{2}(\mu) }\\\\\frac{1}{(\frac{1}{cos(\mu)})^{2} }\\\\\frac{1}{\frac{1^{2} }{cos^{2} (\mu)} }\\\\cos^{2} (\mu)\\\\\frac{sen^{2}(\mu)+cos^{2}(\mu) }{tan^{2}(\mu)+1 }=cos^{2} (\mu)$

g)

$\frac{tan(\sigma)}{sec(\sigma)}\\\\\frac{\frac{sen(\sigma)}{cos(\sigma)} }{\frac{1}{cos(\sigma)} }\\\\\frac{(sen(\sigma))(cos(\sigma))}{cos(\sigma)} \\\\sen(\sigma) \\\\\frac{tan(\sigma)}{sec(\sigma)}=sen(\sigma)$

h)

$(cos(\lambda))(1-cos^{2}(\lambda))\\\\(cos(\lambda))(sen^{2}(\lambda))$