| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion \[co{{s}^{2}}\text{ }A-si{{n}^{2}}\text{ }A=1\], \[{{\tan }^{2}}A-{{\sec }^{2}}A=1\] are trigonometric identities. |
| Reason An equation involving trigonometric ratios of an angle is called a trigonometric identity. It is true for all values of the angles involved. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is false.
D) A is false; R is true.
Correct Answer: D
Solution :
| We have, \[{{\cos }^{2}}A-{{\sin }^{2}}A=1\] |
| Put \[A=45{}^\circ\], we get |
| \[{{\cos }^{2}}45{}^\circ -{{\sin }^{2}}45{}^\circ =0\] |
| and \[{{\tan }^{2}}A-{{\sec }^{2}}A=1\] |
| Put \[A=45{}^\circ ,\,{{\tan }^{2}}45{}^\circ -{{\sec }^{2}}45{}^\circ =-1\] |
| These are not trigonometric but identities. Assertion is false but Reason is true. |
You need to login to perform this action.
You will be redirected in
3 sec
