Question

Assertion :Statement 1: $\cos 1<\cos 7$. Reason: Statement 2: $1<7$.

• A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
• B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
• C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
• D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Answer 1

The correct option is B Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1

Let $x=\cos 1-\cos 7=2\sin 4\sin 3$

$\because 3\in (0,\pi )$

$\Rightarrow \sin 3>0$ ...(1)

$\because 4\in (\pi ,2\pi )$

$\Rightarrow \sin 4<0$ ...(2)
From (1) & (2)
$\sin 3\sin 4<0$

$\therefore \cos 1-\cos 7<0$
Ans: B