Assertion and reason

Exercise and reference answers

Questions

1. Reason

   sec²x equals 1 + tan²x, and a square is never negative.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   sec²x is never less than 1.

2. Reason

   sine is odd and cosine is even.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   sin and cos behave differently under a sign change of x.

3. Reason

   sin(−x) = −sin x.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   cos(−x) = −cos x.

4. Reason

   π radians corresponds to 180 degrees.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Angles can be measured in radians instead of degrees.

Explanation