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

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