If (sin θ + cosec θ)2 + (cos θ + sec θ)2 = k + tan2 θ + cot2 θ

1.	If (sin θ + cosec θ)2 + (cos θ + sec θ)2 = k + tan2 θ + cot2 θ, then the value of k is equal to:1. 52. 73. 24. 9
Answer» Correct Answer - Option 2 : 7 Given: (sin θ + cosec θ)² + (cos θ + sec θ)² = k + tan²θ + cot²θ Formula used: (a + b)² = a² + 2ab + b² sin² θ + cos² θ = 1 sec² θ - tan² θ = 1 cosec² θ - cot² θ = 1 sin θ × cosec θ = 1 cos θ × sec θ = 1 Calculation: According to the question, sin² θ + cosec² θ + 2 × sin θ × cosec θ + cos² θ + sec² θ + 2 × cos θ × sec θ = k + tan² θ + cot² θ ⇒ 1 + cosec² θ + 2 × 1 + sec² θ + 2 × 1 = k + tan² θ + cot² θ ⇒ 5 + (cosec² θ - cot² θ) + (sec² θ - cot² θ) = k ⇒ 5 + 1 + 1 = k ⇒ k = 7 ∴ The value of k is 7.

If (sin θ + cosec θ)2 + (cos θ + sec θ)2 = k + tan2 θ + cot2 θ, then the value of k is equal to:1. 52. 73. 24. 9

Answer» Correct Answer - Option 2 : 7

Given:

(sin θ + cosec θ)² + (cos θ + sec θ)² = k + tan²θ + cot²θ

Formula used:

(a + b)² = a² + 2ab + b²

sin² θ + cos² θ = 1

sec² θ - tan² θ = 1

cosec² θ - cot² θ = 1

sin θ × cosec θ = 1

cos θ × sec θ = 1

Calculation:

According to the question,

sin² θ + cosec² θ + 2 × sin θ × cosec θ + cos² θ + sec² θ + 2 × cos θ × sec θ = k + tan² θ + cot² θ

⇒ 1 + cosec² θ + 2 × 1 + sec² θ + 2 × 1 = k + tan² θ + cot² θ

⇒ 5 + (cosec² θ - cot² θ) + (sec² θ - cot² θ) = k

⇒ 5 + 1 + 1 = k

⇒ k = 7

∴ The value of k is 7.