Question

How do I this math problem? If tan8 theta = cot 7 theta then theta =?

Answer 1

Given:

$\tan 8\theta =\cot 7\theta$

To find:

The value of $\theta$.

Solution:

We have,

$\tan 8\theta =\cot 7\theta$

We know that, $\cot \theta =\tan (90^\circ -\theta)$.

Using the trigonometric property, we get

$\tan 8\theta =\tan (90^\circ -7\theta)$

On comparing both sides, we get

$8\theta =90^\circ -7\theta$

$8\theta +7\theta=90^\circ$

$15\theta=90^\circ$

Divide both sides by 15.

$\theta=\dfrac{90^\circ}{15}$

$\theta=6^\circ$

Therefore, the value of $\theta$ is 6 degrees.