Answer:
B) [tex]\frac{1}{cot\theta}[/tex].
Step-by-step explanation:
We have to find out the reciprocal of [tex]tan\theta[/tex].
We have drawn a triangle for your reference.
In which [tex]\angle C=\theta[/tex]
AB = opposite side
BC = adjacent side
CA = hypotenuse
Since we know that the [tex]tan\theta[/tex] is equal to opposite side upon adjacent side.
[tex]tan\theta=\frac{opposite\ side}{adjacent\ side}=\frac{AB}{BC}[/tex]
Or [tex]tan\theta=\frac{sin\theta}{cos\theta} \ \ \ \ equation\ 1[/tex]
Where as the [tex]cot\theta[/tex] is equal to adjacent side upon opposite side.
Therefore,
[tex]cot\theta=\frac{adjacent\ side}{opposite\ side}=\frac{BC}{AB}[/tex]
Or [tex]cot\theta=\frac{cos\theta}{sin\theta} \ \ \ \ equation \ 2[/tex]
From equation 1 and equation 2 we can say that;
[tex] tan\theta=\frac{1}{cot\theta}[/tex]
Hence [tex]tan\theta=\frac{1}{cot\theta}[/tex].
