If tan θ + cot θ = 2, then tan2θ + cot2θ is equal to: 1. 1 2. 2 3. 4 4. 8

Given, tan θ + cot θ = 2 Square on both sides, ⇒ (tan θ + cot θ)2 = 22 ⇒ tan2 θ + cot2 θ + 2 tan θ cot θ = 4 ⇒ tan2 θ + cot2 θ + 2 tan θ = 4 ⇒ tan2 θ + cot2 θ + 2 = 4 ⇒ tan2 θ + cot2 θ = 4 - 2 ⇒ tan2 θ + cot2 θ = 2 Hence, option 2 is the correct option.

Mathematics

If tan θ + cot θ = 2, then tan²θ + cot²θ is equal to:
1
2
4
8

Trigonometric Identities

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Answer

Given,

tan θ + cot θ = 2

Square on both sides,

⇒ (tan θ + cot θ)² = 2²

⇒ tan² θ + cot² θ + 2 tan θ cot θ = 4

⇒ tan² θ + cot² θ + 2 tan θ $\dfrac{1}{\tan \theta}$ = 4

⇒ tan² θ + cot² θ + 2 = 4

⇒ tan² θ + cot² θ = 4 - 2

⇒ tan² θ + cot² θ = 2

Hence, option 2 is the correct option.

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Mathematics

If tan θ + cot θ = 2, then tan²θ + cot²θ is equal to:
1
2
4
8

Trigonometric Identities

Answer

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