(sec θ - cos θ) 2 - (sec θ + cos θ) 2 is equal to : 1. 4 2. 2 3. -2 4. -4

Solving, ⇒ (sec θ - cos θ) 2 - (sec θ + cos θ) 2 ⇒ (sec θ - cos θ + sec θ + cos θ)[(sec θ - cos θ) - (sec θ + cos θ)] [∵ a 2 - b 2 = (a + b)(a - b)] ⇒ (sec θ - cos θ + sec θ + cos θ)(sec θ - sec θ - cos θ - cos θ) ⇒ 2 sec θ.(-2 cos θ) ⇒ -4.sec θ.cos θ ⇒ ⇒ -4. Hence, Option 4 is the correct option.

Mathematics

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

Trigonometric Identities

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Answer

Solving,

⇒ (sec θ - cos θ)² - (sec θ + cos θ)²

⇒ (sec θ - cos θ + sec θ + cos θ)[(sec θ - cos θ) - (sec θ + cos θ)] [∵ a² - b² = (a + b)(a - b)]

⇒ (sec θ - cos θ + sec θ + cos θ)(sec θ - sec θ - cos θ - cos θ)

⇒ 2 sec θ.(-2 cos θ)

⇒ -4.sec θ.cos θ

⇒ $-4 \times \dfrac{1}{\text{cos θ}} \times \text{cos θ}$

⇒ -4.

Hence, Option 4 is the correct option.

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Mathematics

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

Trigonometric Identities

Answer

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

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

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a × b = 1
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