If tan θ + cot θ = 2, then find the value of tan⁵³ θ + cot³⁸θ.

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Graduate Level) Official Paper (Held On: 20 Jun, 2024 Shift 3)

Answer 1

Given:

If tan θ + cot θ = 2

Formula Used:

tan² θ + cot² θ = 2

Calculation:

Let tan θ = x, then cot θ = 1/x

Given: x + 1/x = 2

⇒ x² + 1 = 2x

⇒ x² - 2x + 1 = 0

⇒ (x - 1)² = 0

⇒ x = 1

So, tan θ = 1 and cot θ = 1

Now, tan ⁵³θ + cot ³⁸θ

Since tan(90° - θ) = cot θ

53θ = 90° - 38θ

⇒ tan ⁵³θ = cot ³⁸θ

⇒ tan ⁵³ θ + cot ³⁸θ = 1 + 1

⇒ 2

The correct answer is option 3.

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