MCQ
The maximum value of the expression $E = sin \theta + cos \theta + sin2 \theta$ is-
- A$\tan \frac{\pi }{4}$
- B$\tan \frac{\pi }{3}$
- C$\tan \frac{\pi }{8}$
- ✓$\tan \frac{3\pi }{8}$
Let $t=\sin \theta+\cos \theta$
$-\sqrt{2} \leq t \leq \sqrt{2}$
$E=t+t^{2}-1$
$=\left(t+\frac{1}{2}\right)^{2}-\frac{5}{4} $
$\Rightarrow E_{\max }=\left(\sqrt{2}+\frac{1}{2}\right)^{2}-\frac{5}{4}$
$=1+\sqrt{2}=\tan \frac{3 \pi}{8}$
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$STATEMENT-1$ : If line $\mathrm{L}_1$ is a chord of circle $\mathrm{C}$, then line $\mathrm{L}_2$ is not always a diameter of circle $\mathrm{C}$. and
$STATEMENT-2$ : If line $\mathrm{L}_1$ is a diameter of circle $\mathrm{C}$, then line $\mathrm{L}_2$ is not a chord of circle $\mathrm{C}$.