Which of the following is equal to $cot θ$ ?

\frac{s i n θ}{c o s θ}

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\frac{c o s θ}{s i n θ}

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\frac{s i n θ}{t a n θ}

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\frac{t a n θ}{s e c θ}

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Solution

The correct option is B $\frac{c o s θ}{s i n θ}$
We know that,
$sin θ = \frac{o p p o s i t e s i d e}{h y p o t e n u s e}$
$cos θ = \frac{a d j a c e n t s i d e}{h y p o t e n u s e}$
$cot θ = \frac{a d j a c e n t s i d e}{o p p o s i t e s i d e}$

Now, $\frac{c o s θ}{s i n θ} = \frac{a d j a c e n t s i d e}{h y p o t e n u s e} \times \frac{h y p o t e n u s e}{o p p o s i t e s i d e}$
So, $cot θ = \frac{c o s θ}{s i n θ} = \frac{a d j a c e n t s i d e}{o p p o s i t e s i d e}$

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