Question

Assertion :Statement 1: If $a,b,cϵR$ and not all equal, then $\sec \theta =\frac{(bc+ca+ab)}{(a^2+b^2+c^2)}$ Reason: Statement 2: $\sec \theta \le -1$ or $\sec \theta \ge 1$

• 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 D STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Consider $y=a^2{+b}^2{+c}^2-ab-bc-ac\Rightarrow y=\frac{{(a-b)}^2+{(b-c)}^2+{(a-c)}^2}{2}\ge 0\Rightarrow \frac{ab+bc+ac}{a^2{+b}^2{+c}^2}\le 1\Rightarrow \sec \theta \le 1$
Since $\sec \theta \le -1or\sec \theta \ge 1$
Therefore $\sec \theta =\frac{ab+bc+ac}{a^2{+b}^2{+c}^2}$ is not true
Ans: D