Question

Find the angle $\theta$ whose cosine is equal to its tangent

• A. $\theta ={\sin }^{-1}\left(2\sin {18}^0\right)$
• B. $\theta ={\sin }^{-1}\left(2\sin {36}^0\right)$
• C. $\theta ={\sin }^{-1}\left(3\sin {18}^0\right)$
• D. $\theta ={\sin }^{-1}\left(2\sin {54}^0\right)$

Answer 1

The correct option is A $\theta ={\sin }^{-1}\left(2\sin {18}^0\right)$

Given, $\cos \theta =\tan \theta$

$\Rightarrow {\cos }^2\theta =\sin \theta$

$1-{\sin }^2\theta =\sin \theta$

${\sin }^2\theta +\sin \theta -1=0$

$\sin \theta =\frac{-1\pm \sqrt{5}}{2}=2\frac{\sqrt{5}-1}{4}=2\sin {18}^0$

$\theta ={\sin }^{-1}\left(2\sin {18}^0\right)$