Mathematics - Trigonometric Equation Question with Solution | TestHub

Let $\mathrm{A}=\{\theta :\sin \theta =\tan \theta \}$ and $\mathrm{B}=\{\theta :\cos \theta =1\}$ Now, $A=\left\{\theta :\sin \theta =\frac{\sin \theta }{\cos \theta }\right\}$ $=\{\theta :\sin \theta (\cos \theta -1)=0\}$ $=\{\theta =0,\pi ,2\pi ,3\pi ,\dots \dots \}$ For $\mathrm{B}:\cos \theta =1\Rightarrow \theta =\pi ,2\pi ,4\pi ,\dots \dots$ This shows that $\mathrm{A}$ is not contained in B. i.e. $\mathrm{A}\not\subset \mathrm{B}$. but $\mathrm{B}\subset \mathrm{A}$.