Question

Let $y=4\sin x+\cos 2x+3$ then

• A. graph of $y$ lies above $y=–1$
• B. graph of $y$ lies above $y=–5$
• C. graph of $y$ lies below $y=5$
• D. graph of $y$ lies below $y=13$

Answer 1

Answer: (B), (D)

The correct options are
B graph of $y$ lies above $y=–5$
D graph of $y$ lies below $y=13$

$y=4\sin x+1-2{\sin }^{2}x+3$

$=4-2({\sin }^{2}x-2\sin x)$

$=6-2(\sin x-1{)}^2$

$y_{\text{max}}=6$

$y_{\text{min}}=-2$