(cot A - cot B) 2 + (1 + cot A cot B) 2 is equal to : 1. sec 2 A - cos 2 A 2. sec 2 A - cosec 2 A 3. (1 + tan A) 2 - (1 - cot A) 2 4. cosec 2 A . cosec 2 B

Solving, ⇒ (cot A - cot B) 2 + (1 + cot A cot B) 2 ⇒ cot 2 A + cot 2 B - 2 cot A cot B + 1 + cot 2 A . cot 2 B + 2 cot A cot B ⇒ cot 2 A + cot 2 A . cot 2 B + 1 + cot 2 B ⇒ cot 2 A(1 + cot 2 B) + (1 + cot 2 B) ⇒ (1 + cot 2 B)(1 + cot 2 A) ⇒ ⇒ Substituting, sin 2 θ + cos 2 θ = 1, we get : ⇒ ⇒ cosec 2 B . cosec 2 A Hence, Option 4 is the correct option.

Mathematics

(cot A - cot B)² + (1 + cot A cot B)² is equal to :
sec² A - cos² A
sec² A - cosec² A
(1 + tan A)² - (1 - cot A)²
cosec² A . cosec² B

Trigonometric Identities

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Mathematics

(cot A - cot B)² + (1 + cot A cot B)² is equal to :
sec² A - cos² A
sec² A - cosec² A
(1 + tan A)² - (1 - cot A)²
cosec² A . cosec² B

Trigonometric Identities

Related Questions

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Prove that:
(sec A - tan A)² (1 + sin A) = (1 - sin A)

Mathematics

(cot A - cot B)2 + (1 + cot A cot B)2 is equal to :sec2 A - cos2 Asec2 A - cosec2 A(1 + tan A)2 - (1 - cot A)2cosec2 A . cosec2 B

Trigonometric Identities

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(sec θ - cos θ)2 - (sec θ + cos θ)2 is equal to :42-2-4

Prove that:(sec A - tan A)2 (1 + sin A) = (1 - sin A)

(cot A - cot B)² + (1 + cot A cot B)² is equal to :
sec² A - cos² A
sec² A - cosec² A
(1 + tan A)² - (1 - cot A)²
cosec² A . cosec² B

(sec θ - cos θ)² - (sec θ + cos θ)² is equal to :
4
2
-2
-4

Prove that:
(sec A - tan A)² (1 + sin A) = (1 - sin A)