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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.
Solution
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.
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