Given:
[tex]\tan 8\theta =\cot 7\theta[/tex]
To find:
The value of [tex]\theta[/tex].
Solution:
We have,
[tex]\tan 8\theta =\cot 7\theta[/tex]
We know that, [tex]\cot \theta =\tan (90^\circ -\theta)[/tex].
Using the trigonometric property, we get
[tex]\tan 8\theta =\tan (90^\circ -7\theta)[/tex]
On comparing both sides, we get
[tex]8\theta =90^\circ -7\theta[/tex]
[tex]8\theta +7\theta=90^\circ [/tex]
[tex]15\theta=90^\circ [/tex]
Divide both sides by 15.
[tex]\theta=\dfrac{90^\circ}{15}[/tex]
[tex]\theta=6^\circ[/tex]
Therefore, the value of [tex]\theta[/tex] is 6 degrees.
