| 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 The equation \[{{\sec }^{2}}\theta =\frac{4xy}{{{\left( x+y \right)}^{2}}}\] is only possible when \[x=y\]. |
| Reason \[{{\sec }^{2}}\theta >1\]and therefore \[{{\left( x-y \right)}^{2}}<0\]. |
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: A
Solution :
| We know that, |
| \[{{\cos }^{2}}\theta \le 1\] |
| \[{{\sec }^{2}}=\frac{4xy}{{{\left( x+y \right)}^{2}}}\ge 1\] |
| \[\Rightarrow 4xy\ge {{\left( x+y \right)}^{2}}\] |
| \[\Rightarrow {{\left( x-y \right)}^{2}}\le 0\] |
| Assertion is true and Reason is true and is the correct explanation of Assertion. |
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