Respuesta :
we are given
[tex] \frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)} =cot(\theta) [/tex]
We will simplify left side and make it equal to right side
Left side:
[tex] \frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)} [/tex]
we can use trigonometric identity
[tex] 1+cot^2(\theta)=csc^2(\theta) [/tex]
we can replace it
[tex] \frac{(csc^2(\theta))*tan(\theta)}{sec^2(\theta)} [/tex]
we know that
csc=1/sin and sec=1/cos
so, we can replace it
and we get
[tex] \frac{cos^2(\theta)tan(\theta)}{sin^2(\theta)} [/tex]
now, we know that
tan =sin/cos
[tex] \frac{cos^2(\theta)*sin(\theta)}{sin^2(\theta)*cos(\theta)} [/tex]
we can simplify it
and we get
[tex] \frac{cos(\theta)}{sin(\theta)} [/tex]
we can also write it as
[tex] =cot(\theta) [/tex]
Right Side:
[tex] cot(\theta) [/tex]
we can see that
left side = right side
so,
[tex] \frac{(1+cot^2(\theta))*tan(\theta)}{sec^2(\theta)} =cot(\theta) [/tex]......Answer
