Solve for x sec(x)=0

Problem

sec(x)=0

Solution

1. Rewrite the secant function in terms of the cosine function using the reciprocal identity.

sec(x)=1/cos(x)

2. Set the new expression equal to the given value.

1/cos(x)=0

3. Analyze the fraction to determine if it can ever equal zero. A fraction is equal to zero only if its numerator is zero.

1≠0

4. Conclude that since the numerator is a constant 1 there is no value of x that can make the expression equal to zero. Furthermore, the range of the secant function is (−∞,−1]∪[1,∞) which does not include zero.

Final Answer

sec(x)=0⇒No solution

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