Question

Assertion :The function f(x) = cos x is symmetric about the line x=0 Reason: Every even function is symmetric about y-axis

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

Answer 1

The correct option is A Both Assertion and Reason are true and Reason is the correct explanation for Assertion

The function f(x) = cos x is a even function as cos(x)=cos(-x) thus

f(x)=f(-x)

if a function is symmetric about any x=a then we say that

f(x)=f(a-x)

thus in the question f(x)=f(0-x). Therefore it is symmetric about x=0

the statement f(x)=f(0-x) is true for every even function therefore any even function is symmetric about x=0 that is y-axis.