Question

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

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

$a^2+b^2+c^2-ab-bc-ca$

$=\frac{1}{2}[2a^2+2b^2+2c^2-2ab-2bc-2ca]$

$=\frac{1}{2}[{(a-b)}^2+{(b-c)}^2+{(c-a)}^2]>0$

$\therefore a^2+b^2+c^2>[ab+bc+ca]$

$\Rightarrow 0<\frac{ab+bc+ca}{a^2+b^2+c^2}<1$

$\therefore$ Assertion is wrong reason is correct