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
0 Comments