Question

Statement A (Assertion): For 0 < θ ≤ 90°, cosec θ – cot θ and cosec θ + cot θ are reciprocal of each other.

Statement R (Reason): cosec² θ – cot² θ = 1

Options

• Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true; but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).

Explanation:

∵ cosec² θ – cot² θ = 1

`\implies` (cosec θ – cot θ) (cosec θ + cot θ) = 1

`\implies` (cosec θ – cot θ) = `1/("cosec"  θ + cot θ)`

∴ It is clear that cosec θ – cot θ and cosec θ + cot θ are reciprocal of each other.