Question : If $\cos\theta = \frac{35}{37}$, then what is the value of $\cot \theta$?
Option 1: $\frac{12}{35}$
Option 2: $\frac{35}{12}$
Option 3: $\frac{37}{12}$
Option 4: $\frac{12}{37}$
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Correct Answer: $\frac{35}{12}$
Solution :
Given: $\cos \theta = \frac{35}{37}$,
$\cos\theta = \frac{\text{Base}}{\text{Hypotenuse}}$
Let base = 35k and hypotenuse = 37k
Using Pythagoras theorem,
$AB =\sqrt{(37k)^{2}-(35k)^{2}} = 12k$
$\therefore\cot \theta = \frac{\text{Base}}{\text{Perpendicular}}$ = $\frac{35}{12}$
Hence, the correct answer is $\frac{35}{12}$.
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