| Consider the following. |
| I. \[{{\sin }^{2}}1{}^\circ +{{\cos }^{2}}1{}^\circ =1\] |
| II. \[{{\sec }^{2}}33{}^\circ -{{\cot }^{2}}57{}^\circ =\text{cose}{{\text{c}}^{2}}37{}^\circ -{{\tan }^{2}}53{}^\circ \] |
| Which of the above statement is/are correct? |
A) Only I
B) Only II
C) Both I and II
D) Neither I nor II
Correct Answer: A
Solution :
| We know that, \[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1\]is true. |
| I. \[{{\sin }^{2}}1{}^\circ +{{\cos }^{2}}1{}^\circ =1\] which is true. |
| II. \[{{\sec }^{2}}33{}^\circ -{{\cot }^{2}}57{}^\circ =\text{cose}{{\text{c}}^{2}}37{}^\circ -{{\tan }^{2}}53{}^\circ \] |
| Now, \[{{\sec }^{2}}\,\,(90{}^\circ -57{}^\circ )=\text{cose}{{\text{c}}^{2}}57{}^\circ \] |
| and \[{{\cot }^{2}}57{}^\circ ={{\cot }^{2}}\,\,(90{}^\circ -33{}^\circ )={{\tan }^{2}}33{}^\circ \] |
| \[\therefore \]\[{{\sec }^{2}}33{}^\circ -{{\cot }^{2}}57{}^\circ =\text{cose}{{\text{c}}^{2}}57{}^\circ -{{\tan }^{2}}33{}^\circ \] |
| II is not true. |
You need to login to perform this action.
You will be redirected in
3 sec
