If tan∝ + cot∝ = 2, then the value of tan13∝ + cot13∝ is ______.

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

Answer : b ) 2

Explaination :

Given : tan∝ + cot∝ = 2

 tan∝ + 1/tan∝=2

tan2∝ + 1/tan∝ = 2

tan2∝ + 1 = 2tan∝

tan2∝ – 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

∴ tan13∝ + cot13

= (1)3 + (1)3 = 1+1 = 2

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