If tan∝ + cot∝ = 2, then the value of tan^{13}∝ + cot^{13}∝ is **__**____.

a) 13 b) 2 c) 1 d) 0

Answer : b ) 2

Explaination :

Given : tan∝ + cot∝ = 2

**⇒** tan∝ + 1/tan∝=2

**⇒** tan^{2}∝ + 1/tan∝ = 2

**⇒** tan^{2}∝ + 1 = 2tan∝

**⇒** tan^{2}∝ – 2tan∝ + 1 = 0

**⇒** (tan)^{2} – 2(tan∝) ☓ 1 + (1)^{2} = 0

**⇒** (tan∝ – 1)^{2} = 0

Taking square root on both sides, we get

**⇒** tan∝ – 1 = 0

**⇒** tan∝ = 1

∴ cot∝ = 1/tan∝ = 1/1 = 1

∴ tan^{13}∝ + cot^{13}∝

= (1)^{3} + (1)^{3} = 1+1 = 2

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