Question

If tan5theta.tan4theta=1,then theta =

Answer 1

Hey mate,

Here is ur answer,


Let theta be A.

Tan5A.Tan4A =1.

We know that,

If TanA. TanB=1. Then A+B =90.

So, 5A+4A =90.

=> 9A =90.

=> A =10.


:-)Hope it helps u.

Answer 2

$\tan( 5\theta) . tan(4\theta) = 1 \\ \tan(5\theta) = \frac{1}{ \tan(4\theta) } = \cot(4\theta) = \tan(90 - 4\theta) \\ 5\theta = 90 - 4\theta \\ 9\theta = 90 \\ \theta = 10 \: degrees$