Question

Assertion :If $\sec \theta +\cos \theta =2$ , then ${\sec }^n\theta +{\cos }^n\theta =2^n$ Reason: If $a+b=2,ab=1$ ,then $a=b=1$

• 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 false but Reason is true

Answer 1

The correct option is D Assertion is false but Reason is true

$a+b=2$

$ab=1$

$b=\frac{1}{a}$

$a+\frac{1}{a}=2$

$a^2-2a+1=0$

$a=1$

or $b=1$

Reason is true.

Assertion : When $a=\sec \theta ,b=\cos \theta$

So $\sec \theta =1,\cos \theta =1$

${\sec }^n\theta +{\cot }^n\theta =2$ and not $2^n$

Hence assertion is false and reason is true