The value of sec (90° – A) – cot A cos (90° – A) tan (90° – A) is :sec (90° – A) – cot A cos (90° – A) tan (90° – A) का मान है :

1. Atan A
2. Bcot A
3. Ccos A
4. Dsin A

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Correct answer: D. sin A

Explanation

Using complementary angles: sec(90° − A) = cosec A, cos(90° − A) = sin A and tan(90° − A) = cot A. The expression becomes cosec A − cot A · sin A · cot A = 1/sin A − cos²A/sin A = (1 − cos²A)/sin A = sin²A/sin A = sin A.पूरक कोणों के सूत्रों से: sec(90° − A) = cosec A, cos(90° − A) = sin A तथा tan(90° − A) = cot A। व्यंजक बनता है cosec A − cot A · sin A · cot A = 1/sin A − cos²A/sin A = (1 − cos²A)/sin A = sin²A/sin A = sin A।