Geometry

Trigonometry

Medium

core

The value of $\cot\left(\cos^{-1}\frac{7}{25}\right)$ is

$\frac{25}{24}$

$\frac{24}{25}$

$\frac{7}{25}$

$\frac{7}{24}$

✅ Correct Option: 4

Let $\theta = \cos^{-1}\frac{7}{25}$

Then $\cos\theta = \frac{7}{25}$

Consider a right triangle where:

Adjacent side $= 7$

Hypotenuse $= 25$

Using the Pythagorean theorem to find the opposite side:

$(Opposite)^2 + 7^2 = 25^2$

$(Opposite)^2 + 49 = 625$

$(Opposite)^2 = 576$

$Opposite = 24$

The cotangent is given by:

$\cot\theta = \frac{Adjacent}{Opposite}$

$\cot\theta = \frac{7}{24}$

Therefore, $\cot\left(\cos^{-1}\frac{7}{25}\right) = \frac{7}{24}$

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