Question

If (tan theta + cot theta)=5 then (tan^2 theta +cot^2 theta)= ?

Answer 1

Answer:

3

Step-by-step explanation:

If (tan theta + cot theta)=5 then (tan^2 theta +cot^2 theta)= ?

Answer 2

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Given that,

• (tan θ + cot θ) = 5

To find,

• Value of (tan² θ + cot² θ) = ?

➡ (tan θ + cot θ) = 5

• Squaring on both sides.

➡ (tan θ + cot θ)² = (5)²

➡ tan² θ + cot² θ + 2 × tan θ × cot θ = 25

➡ tan² θ + cot² θ + 2 × tan θ × 1/tan θ = 25

➡ tan² θ + cot² θ + 2 = 25

➡ tan² θ + cot² θ = 25 - 2

➡ tan² θ + cot² θ = 23

$\boxed{∴ tan² \: θ + cot² \: θ = 23}$

Step-by-step explanation:

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